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Satoshi Tanaka

Section

Graduate School of Science

Job title

Professor

Degree

researchmap

https://researchmap.jp/satoshi_tanaka

J-GLOBAL ID

201801017179599110

e-Rad No.

90331959

Profile

主に境界値問題について研究しています。

Research History 5

2020/04 - Present

Tohoku University　Graduate School of Science Department of Mathematics　Professor
2014/04 - 2020/04

Okayama University of Science　Faculty of Science　Professor
2009/04 - 2014/03

Okayama University of Science　Faculty of Science　Associate Professor
2004/04 - 2009/03

Okayama University of Science　Faculty of Science　Lecturer
2000/04 - 2004/03

Hachinohe National College of Technology　Lecturer

Education 4

Ehime University　Faculty of Science

1999/04 - 2000/03
Ehime University

1996/04 - 1999/03
Toyama University

1994/04 - 1996/03
Toyama University　Faculty of Science　Department of Mathematics

1990/04 - 1994/03

Committee Memberships 12

Differential Equations and Dynamical Systems　Editor

2022/07 - Present
Tohoku Mathematical Journal　Editor

2020/04 - Present
Differential Equations & Applications　Editor

2017/01 - Present
ヨーロッパ数学会　Reviewer for zbMATH

2007/09 - Present
アメリカ数学会　Reviewer for Mathematical Reviews

2007/05 - Present
雑誌「数学通信」, 非常任編集委員

2024/03 - 2025/02
日本数学会東北支部, 代議員

2024/03 - 2025/02
雑誌「数学通信」　常任編集委員

2023/03 - 2024/02
日本数学会東北支部　評議員

2023/03 - 2024/02
日本数学会　2016年度地方区代議員

2016/03 - 2017/02
FONDECYT　FONDECYT Regular 2016 grant competition 審査員

2015/10 - 2015/12
Croatian Science Foundation　Croatian Science Foundation 審査員

2013/02 - 2013/05

Show all ︎Show first 5

Professional Memberships 2

日本応用数理学会

2021/09 - Present
THE MATHEMATICAL SOCIETY OF JAPAN

Research Interests 5

box-counting dimension
elliptic differential equation
bifurcation
boundary value problem
ordinary differential equation

Research Areas 1

Natural sciences / Mathematical analysis /

Awards 1

The 5th Hukuhara Prize (2013)

2013/12　Division of Functional Equations, The Mathematical Society of Japan　Research on boundary value problems and qualitative properties of solutions to ordinary differential equations and research on neutral differential equations

Papers 59

Uniqueness and multiple existence of positive radial solutions of the Brezis-Nirenberg problem on annular domains in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si19.svg" display="inline" id="d1e1200"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">S</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math> Peer-reviewed

Naoki Shioji, Satoshi Tanaka, Kohtaro Watanabe

Nonlinear Analysis　261　113886-113886　2025/12
Publisher: Elsevier BV
DOI： 10.1016/j.na.2025.113886 　

ISSN： 0362-546X
Uniqueness and multiplicity of positive radial solutions to the super-critical Brezis-Nirenberg problem in an annulus Peer-reviewed

Naoki Shioji, Satoshi Tanaka, Kohtaro Watanabe

Journal of Differential Equations　446　113621-113621　2025/11
Publisher: Elsevier BV
DOI： 10.1016/j.jde.2025.113621 　

ISSN： 0022-0396
Morse index and symmetry-breaking bifurcation of positive solutions to the one-dimensional Liouville type equation with a step function weight Peer-reviewed

Kanako Manabe, Satoshi Tanaka

Nonlinear Differential Equations and Applications NoDEA　32　(5)　2025/07/31
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s00030-025-01115-w 　

ISSN： 1021-9722

eISSN： 1420-9004
Two point boundary value problems for ordinary differential systems with generalized variable exponents operators Peer-reviewed

Marta García-Huidobro, Raúl Manásevich, Jean Mawhin, Satoshi Tanaka

Nonlinear Analysis: Real World Applications　81　104196-104196　2025/02
Publisher: Elsevier BV
DOI： 10.1016/j.nonrwa.2024.104196 　

ISSN： 1468-1218
Asymptotic behavior and monotonicity of the best constant for the Sobolev-Poincaré inequality Peer-reviewed

Ryuji Kajikiya, Mieko Tanaka, Satoshi Tanaka

Communications on Pure and Applied Analysis　24　(6)　1140-1155　2025
Publisher: American Institute of Mathematical Sciences (AIMS)
DOI： 10.3934/cpaa.2025028 　

ISSN： 1534-0392

eISSN： 1553-5258
Nonexistence results for a nonvariational system with variable exponents and existence via blow-up Peer-reviewed

Marta García-Huidobro, Raúl Manásevich, Satoshi Tanaka

Discrete and Continuous Dynamical Systems　45　(11)　4554-4571　2025
Publisher: American Institute of Mathematical Sciences (AIMS)
DOI： 10.3934/dcds.2025067 　

ISSN： 1078-0947

eISSN： 1553-5231
Influence of nonlinearity to box-counting dimensions of spiral orbits for two-dimensional differential systems Peer-reviewed

Masakazu Onitsuka, Satoshi Tanaka

Bulletin des Sciences Mathématiques　192　103417-103417　2024/05
Publisher: Elsevier BV
DOI： 10.1016/j.bulsci.2024.103417 　

ISSN： 0007-4497
Asymptotic behavior and monotonicity of radial eigenvalues for the p-Laplacian Peer-reviewed

Ryuji Kajikiya, Mieko Tanaka, Satoshi Tanaka

Journal of Differential Equations　387　(5)　496-531　2024/04

DOI： 10.1016/j.jde.2024.01.027 　
Periodic solutions for nonlinear systems of Ode's with generalized variable exponents operators Peer-reviewed

M. García-Huidobro, R. Manásevich, J. Mawhin, S. Tanaka

Journal of Differential Equations　388　34-58　2024
Publisher: Elsevier BV
DOI： 10.1016/j.jde.2023.12.040 　

ISSN： 0022-0396
An eigenvalue problem for a variable exponent problem, via topological degree Peer-reviewed

Raul Manasevich, Satoshi Tanaka

Discrete and Continuous Dynamical Systems　2023

DOI： 10.3934/dcds.2023134 　
Multiple existence of positive even solutions for a two point boundary value problem on some very narrow possible parameter set Peer-reviewed

Naoki Shioji, Satoshi Tanaka, Kohtaro Watanabe

Journal of Mathematical Analysis and Applications　513　(1)　126182-126182　2022/09
Publisher: Elsevier BV
DOI： 10.1016/j.jmaa.2022.126182 　

ISSN： 0022-247X
A note on the asymptotic behavior of radial solutions to quasilinear elliptic equations with a Hardy potential Peer-reviewed

Kenta Itakura, Satoshi Tanaka

Proceedings of the American Mathematical Society, Series B　8　(25)　302-310　2021/10/12
Publisher: American Mathematical Society (AMS)
DOI： 10.1090/bproc/100 　

eISSN： 2330-1511

More details Close

<p>The quasilinear elliptic equation with a Hardy potential <disp-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal d normal i normal v left-parenthesis StartAbsoluteValue x EndAbsoluteValue Superscript alpha Baseline StartAbsoluteValue nabla u EndAbsoluteValue Superscript p minus 2 Baseline nabla u right-parenthesis plus StartFraction mu Over StartAbsoluteValue x EndAbsoluteValue Superscript p minus alpha Baseline EndFraction StartAbsoluteValue u EndAbsoluteValue Superscript p minus 2 Baseline u equals 0 in bold upper R Superscript upper N Baseline minus StartSet 0 EndSet"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">d</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> <mml:mi mathvariant="normal">v</mml:mi> </mml:mrow> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>x</mml:mi> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>α</mml:mi> </mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi mathvariant="normal">∇</mml:mi> <mml:mi>u</mml:mi> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>p</mml:mi> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mi mathvariant="normal">∇</mml:mi> <mml:mi>u</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>+</mml:mo> <mml:mfrac> <mml:mi>μ</mml:mi> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>x</mml:mi> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>p</mml:mi> <mml:mo>−</mml:mo> <mml:mi>α</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:mfrac> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>u</mml:mi> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>p</mml:mi> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mspace width="1em" /> <mml:mtext>in</mml:mtext> <mml:mtext> </mml:mtext> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">R</mml:mi> </mml:mrow> </mml:mrow> <mml:mi>N</mml:mi> </mml:msup> <mml:mo>−</mml:mo> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:mn>0</mml:mn> <mml:mo fence="false" stretchy="false">}</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\begin{equation*} {\mathrm {div } }(|x|^\alpha |\nabla u|^{p-2}\nabla u) + \frac {\mu }{|x|^{p-\alpha } }|u|^{p-2}u = 0 \quad \text {in} \ {\mathbf {R } }^N-\{0\} \end{equation*}</mml:annotation> </mml:semantics> </mml:math> </disp-formula> is considered, where <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N element-of bold upper N"> <mml:semantics> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>∈</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">N</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">N\in {\mathbf {N } }</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p greater-than 1"> <mml:semantics> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">p>1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="alpha element-of bold upper R"> <mml:semantics> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>∈</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">R</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">\alpha \in {\mathbf {R } }</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="mu element-of bold upper R minus StartSet 0 EndSet"> <mml:semantics> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mo>∈</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">R</mml:mi> </mml:mrow> </mml:mrow> <mml:mo>−</mml:mo> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:mn>0</mml:mn> <mml:mo fence="false" stretchy="false">}</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mu \in {\mathbf {R } }-\{0\}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In this note, the asymptotic behaviors of radial solutions are obtained divided into three case <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="mu greater-than StartAbsoluteValue left-parenthesis upper N minus p plus alpha right-parenthesis slash p EndAbsoluteValue Superscript p"> <mml:semantics> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mo>></mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>N</mml:mi> <mml:mo>−</mml:mo> <mml:mi>p</mml:mi> <mml:mo>+</mml:mo> <mml:mi>α</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>p</mml:mi> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>p</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">\mu >|(N-p+\alpha )/p|^p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="mu equals StartAbsoluteValue left-parenthesis upper N minus p plus alpha right-parenthesis slash p EndAbsoluteValue Superscript p"> <mml:semantics> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>N</mml:mi> <mml:mo>−</mml:mo> <mml:mi>p</mml:mi> <mml:mo>+</mml:mo> <mml:mi>α</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>p</mml:mi> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>p</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">\mu =|(N-p+\alpha )/p|^p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="mu greater-than StartAbsoluteValue left-parenthesis upper N minus p plus alpha right-parenthesis slash p EndAbsoluteValue Superscript p"> <mml:semantics> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mo>></mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>N</mml:mi> <mml:mo>−</mml:mo> <mml:mi>p</mml:mi> <mml:mo>+</mml:mo> <mml:mi>α</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>p</mml:mi> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>p</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">\mu >|(N-p+\alpha )/p|^p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. This equation also appears as the Euler-Lagrange equation related to the weighted Hardy inequality <disp-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Underscript normal upper Omega Endscripts StartAbsoluteValue nabla u left-parenthesis x right-parenthesis EndAbsoluteValue Superscript p Baseline StartAbsoluteValue x EndAbsoluteValue Superscript alpha Baseline d x greater-than-or-equal-to StartAbsoluteValue StartFraction upper N minus p plus alpha Over p EndFraction EndAbsoluteValue Superscript p Baseline integral Underscript normal upper Omega Endscripts StartAbsoluteValue u left-parenthesis x right-parenthesis EndAbsoluteValue Superscript p Baseline StartAbsoluteValue x EndAbsoluteValue Superscript alpha minus p Baseline d x"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mo>∫</mml:mo> <mml:mi mathvariant="normal">Ω</mml:mi> </mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi mathvariant="normal">∇</mml:mi> <mml:mi>u</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>p</mml:mi> </mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>x</mml:mi> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>α</mml:mi> </mml:msup> <mml:mi>d</mml:mi> <mml:mi>x</mml:mi> <mml:mo>≥</mml:mo> <mml:mstyle scriptlevel="0"> <mml:mrow class="MJX-TeXAtom-OPEN"> <mml:mo maxsize="2.470em" minsize="2.470em">|</mml:mo> </mml:mrow> </mml:mstyle> <mml:mfrac> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>−</mml:mo> <mml:mi>p</mml:mi> <mml:mo>+</mml:mo> <mml:mi>α</mml:mi> </mml:mrow> <mml:mi>p</mml:mi> </mml:mfrac> <mml:msup> <mml:mstyle scriptlevel="0"> <mml:mrow class="MJX-TeXAtom-CLOSE"> <mml:mo maxsize="2.470em" minsize="2.470em">|</mml:mo> </mml:mrow> </mml:mstyle> <mml:mi>p</mml:mi> </mml:msup> <mml:msub> <mml:mo>∫</mml:mo> <mml:mi mathvariant="normal">Ω</mml:mi> </mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>u</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>p</mml:mi> </mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>x</mml:mi> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>α</mml:mi> <mml:mo>−</mml:mo> <mml:mi>p</mml:mi> </mml:mrow> </mml:msup> <mml:mi>d</mml:mi> <mml:mi>x</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\begin{equation*} \int _\Omega |\nabla u(x)|^p |x|^\alpha dx \ge \Biggl | \frac {N-p+\alpha }{p} \Biggr |^p \int _\Omega |u(x)|^p |x|^{\alpha -p} dx \end{equation*}</mml:annotation> </mml:semantics> </mml:math> </disp-formula> for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u element-of upper C Subscript c Superscript normal infinity Baseline left-parenthesis bold upper R Superscript upper N Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>u</mml:mi> <mml:mo>∈</mml:mo> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mi>c</mml:mi> <mml:mi mathvariant="normal">∞</mml:mi> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">R</mml:mi> </mml:mrow> </mml:mrow> <mml:mi>N</mml:mi> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">u \in C_c^\infty ({\mathbf {R } }^N)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N minus p plus alpha not-equals 0"> <mml:semantics> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>−</mml:mo> <mml:mi>p</mml:mi> <mml:mo>+</mml:mo> <mml:mi>α</mml:mi> <mml:mo>≠</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">N-p+\alpha \ne 0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Omega"> <mml:semantics> <mml:mi mathvariant="normal">Ω</mml:mi> <mml:annotation encoding="application/x-tex">\Omega</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a domain of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="bold upper R Superscript upper N"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">R</mml:mi> </mml:mrow> </mml:mrow> <mml:mi>N</mml:mi> </mml:msup> <mml:annotation encoding="application/x-tex">{\mathbf {R } }^N</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.</p> <p>The rectifiability of oscillatory solutions to the ordinary differential equation with one-dimensional <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Laplacian is also studied, and an answer to an open problem is given.</p>
Uniqueness of positive radial solutions of superlinear elliptic equations in annuli Peer-reviewed

Naoki Shioji, Satoshi Tanaka, Kohtaro Watanabe

Journal of Differential Equations　284　522-545　2021/05
Publisher: Elsevier BV
DOI： 10.1016/j.jde.2021.02.047 　

ISSN： 0022-0396
Rectifiability of orbits for two-dimensional nonautonomous differential systems Peer-reviewed

Masakazu Onitsuka, Satoshi Tanaka

Electronic Journal of Qualitative Theory of Differential Equations　2021　(18)　1-23　2021/03
Publisher: University of Szeged
DOI： 10.14232/ejqtde.2021.1.18 　

eISSN： 1417-3875
On the uniqueness of solutions of a semilinear equation in an annulus Peer-reviewed

Carmen Cortázar, M. García-Huidobro, Pilar Herreros, Satoshi Tanaka

Communications on Pure & Applied Analysis　0　(0)　0-0　2021
Publisher: American Institute of Mathematical Sciences (AIMS)
DOI： 10.3934/cpaa.2021029 　

ISSN： 1553-5258
Perturbations of planar quasilinear differential systems Peer-reviewed

Kenta Itakura, Masakazu Onitsuka, Satoshi Tanaka

Journal of Differential Equations　271　216-253　2021/01

DOI： 10.1016/j.jde.2020.08.024 　

ISSN： 0022-0396

eISSN： 1090-2732
Positive Solutions for Systems of Quasilinear Equations with Non-homogeneous Operators and Weights Invited Peer-reviewed

Marta Garcia-Huidobro, Raul Manasevich, Satoshi Tanaka

Advanced Nonlinear Studies　20　(2)　293-310　2020
Symmetry-breaking bifurcation for the one-dimensional Henon equation Peer-reviewed

Satoshi Tanaka

Communications in Contemporary Mathematics　21　(1)　2019

DOI： 10.1142/S0219199717500973 　
Rectifiable and nonrectifiable solution curves of half-linear differential systems Peer-reviewed

Yuki Naito, Mervan Pašić, Satoshi Tanaka

Mathematica Slovaca　68　(3)　575-590　2018/06/26
Publisher: De Gruyter Open Ltd
DOI： 10.1515/ms-2017-0126 　

ISSN： 1337-2211 0139-9918
A complete classification of bifurcation diagrams for a class of (p,q)-Laplace equations Peer-reviewed

Ryuji Kajikiya, Inbo Sim, Satoshi Tanaka

Journal of Mathematical Analysis and Applications　462　(2)　1178-1194　2018/06/15
Publisher: Academic Press Inc.
DOI： 10.1016/j.jmaa.2018.02.049 　

ISSN： 1096-0813 0022-247X
Box-counting dimension of oscillatory solutions to the Emden-Fowler equation Peer-reviewed

Takanao Kanemitsu, Satoshi Tanaka

Differential Equations & Applications　10　(2)　239-250　2018

DOI： 10.7153/dea-2018-10-17 　
Box-counting dimension of solution curves for a class of two-dimensional nonautonomous linear differential systems Peer-reviewed

Masakazu Onitsuka, Satoshi Tanaka

Mathematical Communications　23　(1)　43-60　2018
Symmetry-breaking bifurcation for the Moore–Nehari differential equation Peer-reviewed

Ryuji Kajikiya, Inbo Sim, Satoshi Tanaka

NoDEA. Nonlinear Differential Equations and Applications　25　(6)　2018

DOI： 10.1007/s00030-018-0545-3 　
Symmetry-breaking bifurcation for the one-dimensional Liouville type equation Peer-reviewed

Satoshi Tanaka

JOURNAL OF DIFFERENTIAL EQUATIONS　263　(10)　6953-6973　2017/11

DOI： 10.1016/j.jde.2017.07.033 　

ISSN： 0022-0396

eISSN： 1090-2732
CHARACTERISTIC EQUATION FOR AUTONOMOUS PLANAR HALF-LINEAR DIFFERENTIAL SYSTEMS Peer-reviewed

M. Onitsuka, S. Tanaka

ACTA MATHEMATICA HUNGARICA　152　(2)　336-364　2017/08

DOI： 10.1007/s10474-017-0722-6 　

ISSN： 0236-5294

eISSN： 1588-2632
Rectifiability of Solutions for a Class of Two-Dimensional Linear Differential Systems Peer-reviewed

Masakazu Onitsuka, Satoshi Tanaka

MEDITERRANEAN JOURNAL OF MATHEMATICS　14　(2)　2017/04

DOI： 10.1007/s00009-017-0854-5 　

ISSN： 1660-5446

eISSN： 1660-5454
BIFURCATION OF POSITIVE SOLUTIONS FOR THE ONE-DIMENSIONAL (p, q)-LAPLACE EQUATION Peer-reviewed

Ryuji Kajikiya, Mieko Tanaka, Satoshi Tanaka

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS　2017　(Paper No. 107)　2017/04

ISSN： 1072-6691
Nonrectifiable oscillatory solutions of second order linear differential equations Peer-reviewed

Takanao Kanemitsu, Satoshi Tanaka

Archivum Mathematicum　53　(4)　193-201　2017
Publisher: Masarykova Universita
DOI： 10.5817/AM2017-4-193 　

ISSN： 1212-5059 0044-8753
Uniqueness of sign-changing radial solutions for Delta u - u plus vertical bar u vertical bar(p-1)u=0 in some ball and annulus Peer-reviewed

Satoshi Tanaka

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS　439　(1)　154-170　2016/07

DOI： 10.1016/j.jmaa.2016.02.036 　

ISSN： 0022-247X

eISSN： 1096-0813
Non-monotone positive solutions of second-order linear differential equations: existence, nonexistence and criteria Peer-reviewed

Mervan Pasic, Satoshi Tanaka

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS　2016　(93)　2016

DOI： 10.14232/ejqtde.2016.1.93 　

ISSN： 1417-3875
Three positive solutions for one-dimensional p-Laplacian problem with sign-changing weight Peer-reviewed

Inbo Sim, Satoshi Tanaka

APPLIED MATHEMATICS LETTERS　49　42-50　2015/11

DOI： 10.1016/j.aml.2015.04.007 　

ISSN： 0893-9659
The exact multiplicity of positive solutions for a class of two-point boundary-value problems with the one-dimensional p-Laplacian Peer-reviewed

Inbo Sim, Satoshi Tanaka

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS　144　(1)　187-203　2014/02

DOI： 10.1017/S0308210512000443 　

ISSN： 0308-2105

eISSN： 1473-7124
Morse index and symmetry-breaking for positive solutions of one-dimensional Hénon type equations Peer-reviewed

Satoshi Tanaka

Journal of Differential Equations　255　(7)　1709-1733　2013/10/01

DOI： 10.1016/j.jde.2013.05.029 　

ISSN： 0022-0396 1090-2732
Fractal oscillations near the domain boundary of radially symmetric solutions of p-Laplace equations Peer-reviewed

Yuki Naito, Mervan Pasic, Darko Zubrinic, Satoshi Tanaka

Contemporary Mathematics　601　325-343　2013
Fractal oscillations of chirp functions and applications to second-order linear differential equations Peer-reviewed

Mervan Pašić, Satoshi Tanaka

International Journal of Differential Equations　2013　(Art. ID 857410)　2013

DOI： 10.1155/2013/857410 　

ISSN： 1687-9643 1687-9651
Fractal oscillations of self-adjoint and damped linear differential equations of second-order Peer-reviewed

Mervan Pasic, Satoshi Tanaka

APPLIED MATHEMATICS AND COMPUTATION　218　(5)　2281-2293　2011/11

DOI： 10.1016/j.amc.2011.07.047 　

ISSN： 0096-3003
Rectifiable oscillations of self-adjoint and damped linear differential equations of second-order Peer-reviewed

Mervan Pasic, Satoshi Tanaka

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS　381　(1)　27-42　2011/09

DOI： 10.1016/j.jmaa.2011.03.051 　

ISSN： 0022-247X
EVENTUALLY POSITIVE SOLUTIONS OF FIRST ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH A DEVIATING ARGUMENT Peer-reviewed

T. Sakamoto, S. Tanaka

ACTA MATHEMATICA HUNGARICA　127　(1-2)　17-33　2010/04

DOI： 10.1007/s10474-010-9064-3 　

ISSN： 0236-5294
On the uniqueness of positive solutions for two-point boundary value problems of Emden-Fowler differential equations Peer-reviewed

Satoshi Tanaka

Mathematica Bohemica　135　(2)　189-198　2010
Uniqueness and nonuniqueness of nodal radial solutions of sublinear elliptic equations in a ball Peer-reviewed

Satoshi Tanaka

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS　71　(11)　5256-5267　2009/12

DOI： 10.1016/j.na.2009.04.009 　

ISSN： 0362-546X
An identity for a quasilinear ODE and its applications to the uniqueness of solutions of BVPs Peer-reviewed

Satoshi Tanaka

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS　351　(1)　206-217　2009/03

DOI： 10.1016/j.jmaa.2008.09.069 　

ISSN： 0022-247X
Sharp conditions for the existence of sign-changing solutions to equations involving the one-dimensional p-Laplacian Peer-reviewed

Yuki Naito, Satoshi Tanaka

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS　69　(9)　3070-3083　2008/11

DOI： 10.1016/j.na.2007.09.002 　

ISSN： 0362-546X
Uniqueness of nodal radial solutions of superlinear elliptic equations in a ball Peer-reviewed

Satoshi Tanaka

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS　138　(6)　1331-1343　2008

DOI： 10.1017/S0308210507000431 　

ISSN： 0308-2105
ON THE UNIQUENESS OF SOLUTIONS WITH PRESCRIBED NUMBERS OF ZEROS FOR A TWO-POINT BOUNDARY VALUE PROBLEM Peer-reviewed

Satoshi Tanaka

DIFFERENTIAL AND INTEGRAL EQUATIONS　20　(1)　93-104　2007/01

ISSN： 0893-4983
Existence and asymptotic behavior of solutions of nonlinear neutral differential equations Peer-reviewed

S Tanaka

MATHEMATICAL AND COMPUTER MODELLING　43　(5-6)　536-562　2006/03

DOI： 10.1016/j.mcm.2005.08.009 　

ISSN： 0895-7177
Forced oscillation of certain hyperbolic equations with continuous distributed deviating arguments. Peer-reviewed

Satoshi Tanaka, Norio Yoshida

Annales Polonici Mathematici　85　(1)　37-54　2005

DOI： 10.4064/ap85-1-4 　
On the existence of multiple solutions of the boundary value problem for nonlinear second-order differential equations Peer-reviewed

Y Naito, S Tanaka

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS　56　(6)　919-935　2004/03

DOI： 10.1016/j.na.2003.10.020 　

ISSN： 0362-546X
Oscillation criteria for a class of second order forced neutral differential equations. Peer-reviewed

Satoshi Tanaka

Mathematics Journal of Toyama University　27　71-90　2004
Publisher: Toyama University
ISSN： 0916-6009
A oscillation theorem for a class of even order neutral differential equations Peer-reviewed

S Tanaka

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS　273　(1)　172-189　2002/09

DOI： 10.1016/S0022-247X(02)00235-4 　

ISSN： 0022-247X
Oscillation of solutions of first-order neutral differential equations Peer-reviewed

Satoshi Tanaka

Hiroshima Mathematical Journal　32　(1)　79-85　2002
Publisher: Hiroshima University
ISSN： 0018-2079
Existence of positive solutions for a class of higher order neutral functional differential equations Peer-reviewed

S Tanaka

CZECHOSLOVAK MATHEMATICAL JOURNAL　51　(3)　573-583　2001

ISSN： 0011-4642
Oscillation of solutions of even order neutral differential equations Peer-reviewed

Satoshi Tanaka

Dynamic Systems and Applications　9　(3)　353-360　2000
Oscillatory and nonoscillatory solutions of neutral differential equations Peer-reviewed

Satoshi Tanaka

Annales Polonici Mathematici　73　(2)　169-184　2000

DOI： 10.4064/ap-73-2-169-184 　
Existence of positive solutions of higher order nonlinear neutral differential equations Peer-reviewed

Satoshi Tanaka

Rocky Mountain Journal of Mathematics　30　(3)　1139-1149　2000

DOI： 10.1216/rmjm/1021477264 　

ISSN： 0035-7596
A necessary and sufficient condition for the oscillation in a class of even order neutral differential equations Peer-reviewed

Satoshi Tanaka

Electronic Journal of Qualitative Theory of Differential Equations　1-27　2000
Publisher: University of Szeged
DOI： 10.14232/ejqtde.2000.1.4 　

ISSN： 1417-3875
Existence of positive solutions for a class of first-order neutral functional differential equations Peer-reviewed

S Tanaka

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS　229　(2)　501-518　1999/01

ISSN： 0022-247X
Oscillations of solutions to parabolic equations with deviating arguments Peer-reviewed

Satoshi Tanaka, Norio Yoshida

Tamkang Journal of Mathematics　28　(3)　169-181　1997
Oscillation properties of solutions of second order neutral differential equations with deviating arguments Peer-reviewed

Satoshi Tanaka

Analysis (Germany)　17　(2-3)　99-112　1997

DOI： 10.1524/anly.1997.17.23.99 　

ISSN： 2196-6753 0174-4747
Forced oscillations of firs orde nonlinear neutral differential equations Peer-reviewed

Tanaka S

Journal of Applied Analysis　3　(1)　23-41　1997

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Misc. 12

Symmetry-breaking bifurcation of positive solutions to a one-dimensional Liouville type equation

田中敏

数理解析研究所講究録「実領域における常微分方程式の定性的研究」　1993　100-106　2016/04
On the nonuniqueness of positive solutions of boundary value problems for superlinear Emden-Fowler equations (Mathematical Analysis and Functional Equations from New Points of View)

Tanaka Satoshi

RIMS Kokyuroku　1750　70-76　2011/07
Publisher: Kyoto University
ISSN： 1880-2818
On the uniqueness and nonuniqueness of nodal radial solutions of sublinear elliptic equations in a ball (Dynamics of Functional Equations and Mathematical Models)

Tanaka Satoshi

RIMS Kokyuroku　1637　39-46　2009/04
Publisher: Kyoto University
ISSN： 1880-2818
An identity for a quasilinear ordinary differential equation and its applications

田中敏

数理解析研究所講究録「関数方程式論におけるモデリングと複素解析」　1582　18-22　2008/04
On the uniqueness of nodal radial solutions of superlinear elliptic equations in a ball

Satoshi Tanaka

RIMS Kokyuroku　1547　120-124　2007/04
Publisher: Kyoto University
ISSN： 1880-2818
Existence of solutions with prescribed numbers of zeros of boundary value problems for ordinary differential equations with the one-dimensional p-Laplacian

Satoshi Tanaka

RIMS Kokyuroku　1474　162-168　2006/02
Publisher: Kyoto University
ISSN： 1880-2818
On the uniqueness of nodal radial solutions of sublinear elliptic equations in a ball (Functional Equations and Complex Systems)

Tanaka Satoshi

RIMS Kokyuroku　1445　12-18　2005/07
Publisher: Kyoto University
ISSN： 1880-2818
Existence of solutions of two point boundary value problems with concave and convex nonlinearities

Satoshi Tanaka

RIMS Kokyuroku　1254　190-192　2002/04
Publisher: Kyoto University
ISSN： 1880-2818
Oscillatory solutions of neutral differential equations

Satoshi Tanaka

RIMS Kokyuroku　1216　274-281　2001/06
Publisher: Kyoto University
ISSN： 1880-2818
Existence of oscillatory solutions of neutral differential equations

Satoshi Tanaka

RIMS Kokyuroku　1128　82-90　2000/01
Publisher: Kyoto University
ISSN： 1880-2818
Comparison Theorems for Neutral Differential Equations

Satoshi Tanaka

RIMS Kokyuroku　1083　219-230　1999/02
Publisher: Kyoto University
ISSN： 1880-2818
中立型微分方程式のある終局的正値解が存在するための必要十分条件

田中敏

数理解析研究所講究録「非線形の数理と関数方程式」　1034　185-198　1998/04
Publisher: 京都大学
ISSN： 1880-2818

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Presentations 161

Uniqueness and multiplicity of positive radial solutions to the super-critical Brezis-Nirenberg type problem in an annulus

2025/09/16
Energy estimates for least energy solutions of the generalized Henon equation

鈴木啓太, 田中敏

日本数学会 2025 年度年会　2025/03/18
球面上における Emden 方程式の正値解の一意性と非一意性

永井陸, 田中敏

日本数学会 2025 年度年会　2025/03/18
球面上の scalar field 方程式の正値全域解の多重存在性

森田大河, 田中敏

日本数学会 2025 年度年会　2025/03/18
Existence and multiplicity of positive radial solutions to the supercritical Brezis-Nirenberg problem in an annulus Invited

Satoshi Tanaka

Geometric Aspects of Partial Differential Equations　2024/12/08
計算機援用による scalar field 方程式の符号変化球対称解の一意性証明

田中一成, 柏木雅英, 内藤雄基, 田中敏, 渡辺宏太郎

日本数学会 2024 年度秋季総合分科会　2024/09/06
The best constant for the Sobolev-Poincare inequality, II. Monotonicity

2024/09/04
The best constant for the Sobolev-Poincare inequality, I. Asymptotic behavior

2024/09/04
Existence of positive solutions to an eigenvalue problem with a variable

2024/09/04
Box-counting dimension of spiral orbits for two-dimensional nonautonomous

2024/09/03
Uniqueness and nonuniqueness of positive radial solutions to the Brezis- Nirenberg problem in an annulus Invited

Satoshi Tanaka

The 42th Kyushu Symposium on Partial Differential Equations　2024/01/22
p-Laplacian の球対称固有値の漸近挙動と単調性

田中敏

北見工大における微分方程式セミナー（通算第45回）　2023/09/13
On the multiplicity of positive even solutions to the one-dimensional Henon type equation on some very narrow possible parameter set Invited

2023/06/01
Uniqueness and multiplicity of positive solutions to the scalar-field equation on large annuli in the three-dimensional unit sphere Invited

Satoshi Tanaka

2023/05/31
三次元単位球面上の円環領域における scalar-field 方程式の正値解の多重存在 Invited

田中敏

微分方程式における解の漸近挙動の解析とその周辺　2023/03/09
Uniqueness and multiplicity of positive solutions to the scalar-field equation on large annuli in the three-dimensional unit sphere Invited

Satoshi Tanaka

13th Americas Conference on Diff. Equations and Nonlinear Analysis and ICMC Summer Meeting on Differ- ential Equations - 2023 Chapter　2023/02/01
Uniqueness and nonuniqueness of positive radial solutions to the Brezis-Nirenberg problem in an annulus Invited

Satoshi Tanaka

The 41th Kyushu Symposium on Partial Differential Equations　2023/01/22
Existence and multiplicity of positive solutions to the scalar-field equation on large annuli in the three-dimensional sphere Invited

Satoshi Tanaka

CMM PDE Seminar　2022/10/25
Existence and multiplicity of positive solutions to the scalar-field equation on large annuli in the 3-sphere

田中敏, 渡辺宏太郎, 塩路直樹

日本数学会 2022 年度秋季総合分科会　2022/09/13
三次元単位球面内の円環領域上の scalar-field 方程式の正値対称解 Invited

田中敏

広島数理解析セミナー (第 260 回)　2022/07/22
On the uniqueness of positive radial solutions to superlinear elliptic equations in annuli Invited

Satoshi Tanaka

The 23rd Northeastern Symposium on Mathematical Analysis　2022/02/22
1 次元 Henon 型方程式の正値対称解の多重存在 Invited

田中敏

第 5 回精度保証付き数値計算の実問題への応用研究集会 (NVR 2021)　2021/11/28
Multiple existence of positive even function solutions for a two point boundary value problem on some very narrow possible parameter set

2021/09/14
Multiplicity of positive even solutions to the one-dimensional Henon type equation on some very narrow possible parameter set Invited

Satoshi Tanaka

Differential Equations Day on ZOOM　2021/08/18
On a perturbation theory for the planar quasilinear differential system and its application

2021/03/15
1 次元 Henon 方程式の正値対称解のモース指数と対称性破壊分岐について Invited

田中敏

第 4 回精度保証付き数値計算の実問題への応用研究集会 (NVR 2020)　2020/11/29
Perturbation of planar quasilinear differential systems and its application Invited

2020/10/22
Perturbations of quasilinear differential systems Invited

Satoshi Tanaka

2019 International Workshop on Nonlinear PDEs and Its Applications　2019/11/02
Perturbations of half-linear differential systems and its application to quasilinear elliptic equations International-presentation

Satoshi Tanaka

Equadiff 2019　2019/07/09
1次元 Henon 方程式の正値対称解のモース指数と対称性破壊分岐 Invited

田中敏

東北大学応用数理解析セミナー　2019/05/16
Uniqueness of positive radial solutions of superlinear elliptic equations in annuli Invited

Satoshi Tanaka

2019/03/26
Symmetry-breaking bifurcation of positive solutions to the Moore-Nehari differential equation

田中敏, 梶木屋龍治, Inbo Sim

日本数学会2018 年度秋季総合分科会　2018/09/24
Characteristic equation for autonomous planar half-linear differential systems International-presentation Invited

Satoshi Tanaka

2018/09/11
Moore-Nehari 方程式の対称性破壊分岐

田中敏

芝浦工業大学における微分方程式セミナー（通算第41 回）　2018/08/25
Symmetry-breaking bifurcation for the Moore-Nehari differential equation International-presentation Invited

Satoshi Tanaka

The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications　2018/07/07
Bifurcation of positive solutions for two classes of one-dimensional (p,q)-Laplace equations International-presentation Invited

Satoshi Tanaka

NTHU Department of Mathematics Visiting Scholar Colloquium　2018/07/04
Box-counting dimension of discrete spirals and its application to difference equations International-presentation

Satoshi Tanaka

ICDEA 2018　2018/05/24
A complete classification of bifurcation diagrams for a class of (p,q)-Laplace equations

梶木屋龍治, Inbo Sim, 田中敏

日本数学会2018年度年会　2018/03/18
Characteristic equation for autonomous planar half-linear differential systems

田中敏, 鬼塚政一

日本数学会2018年度年会　2018/03/18
Box dimension of solution curves for a class of two-dimensional linear differential systems

鬼塚政一, 田中敏

日本数学会2018年度年会　2018/03/18
Existence of a symmetry-breaking bifurcation point for the one-dimensional Liouville type equation Invited

田中敏

第39 回「南大阪応用数学セミナー」　2017/10/28
Morse index and symmetry-breaking bifurcation of positive solutions to the one-dimensional Liouville type equation International-presentation Invited

Satoshi Tanaka

2017/10/17
Morse index and symmetry-breaking bifurcation of positive solutions to the one-dimensional Liouville type equation International-presentation Invited

Satoshi Tanaka

Nonlinear Analysis, PDEs, and Applications : A Conference in Honor of Yong-Hoon Lee's 60th Birthday　2017/09/23
Symmetry-breaking bifurcation for positive solutions of the one-dimensional Henon equation International-presentation

Satoshi Tanaka

Equadiff 2017　2017/07/25
Asymptotic behavior of solutions to autonomous planar half-linear differential systems Invited

Satoshi Tanaka

International Conference on Differential & Difference Equations and Applications　2017/06
Symmetry-breaking bifurcation for the one-dimensional Henon equation International-presentation Invited

Satoshi Tanaka

2017 International Workshop on Nonlinear PDE and Applications　2017/04
Symmetry-breaking bifurcation for the one-dimensional Henon equation (日本語)

田中敏

2017年度日本数学会年会　2017/03
一次元 Henon 方程式の対称性破壊分岐

田中敏

微分方程式論ワークショップ岐阜2017　2017/03
Symmetry-breaking bifurcation for the one-dimensional Henon equation Invited

田中敏

九州関数方程式セミナー　2017/01
２次元半分線形自励系に付随する特性方程式 International-presentation Invited

田中敏

常微分方程式の定性的理論ワークショップ　2016/09
Bifurcation of positive solutions for the one-dimensional (p,q)-Laplace equation International-presentation Invited

Satoshi Tanaka

The 11th AIMS International Conference on Dynamical Systems, Differential Equations and Applications　2016/07
Morse index and symmetry-breaking bifurcation for the one-dimensional Liouville type equation

田中敏

日本数学会2016年度年会　2016/03
Attractivity, rectifiability and non-rectifiability of solutions for two-dimensional linear differential systems

鬼塚政一, 田中敏

日本数学会2016年度年会　2016/03
１次元リウヴィル型方程式の正値解の対称性の破れとモース指数

田中敏

微分方程式論ワークショップ岐阜 2016　2016/02
Symmetry-breaking for positive solutions of the one-dimensional Liouville type equation International-presentation Invited

Satoshi Tanaka

Workshop on Analysis in Kagurazaka 2016　2016/01
A symmetry-breaking bifurcation for a one-dimensional Liouville type equation International-presentation Invited

Satoshi Tanaka

3rd Chile-Japan Workshop on Nonlinear PDEs　2015/12
Symmetry-breaking bifurcation of positive solutions to a one-dimensional Liouville type equation International-presentation Invited

Satoshi Tanaka

RIMS 研究集会実領域における常微分方程式の定性的研究　2015/11
１次元 Liouville 型方程式の正値解の対称性の破れ

田中敏

富山解析セミナー2015　2015/10
Uniqueness of sign-changing radial solutions for the scalar field equation in some ball and annulus

田中敏

日本数学会2015年度秋季総合分科会　2015/09
Symmetry-breaking bifurcation for one-dimensional Liouville type equations with weights International-presentation Invited

Satoshi Tanaka

Nonlinear PDE Workshop at Tohoku University　2015/09
Uniqueness of sign-changing radial solutions for scalar field equations in some ball and annulus International-presentation

Satoshi Tanaka

Equadiff 2015　2015/07
Uniqueness of sign-changing radial solutions to the scalar field equation in some ball and annulus Invited

田中敏

解析セミナー　2015/06
On the uniqueness of sign-changing radial solutions to the scalar field equation in some ball and annulus International-presentation Invited

Satoshi Tanaka

2015 International Workshop on Nonlinear PDE and Applications　2015/06
スカラー場方程式の符号変化する球対称解の一意性について

田中敏

常微分方程式ワークショップ松山 2015　2015/03
２点境界値問題の正値解の対称性の破れとモース指数 Invited

田中敏

九州関数方程式セミナー　2014/11
A note on the uniqueness of sign-changing radial solutions for scalar field equations International-presentation Invited

Satoshi Tanaka

The 10th AIMS Conference on Dynamical Systems Differential Equations and Applications　2014/07
A note on the uniqueness of sign-changing radial solutions for scalar eld equations in thin annuli Invited

田中敏

なかもず解析セミナー第20回　2014/06
１次元 Henon 型方程式の正値解の対称性の破れ

田中敏

振動理論ワークショップー金沢 2014　2014/03
Uniqueness of nodal radial solutions for a Dirichlet problem with an exponent near 1 in some 2-dimensional annulus International-presentation Invited

Satoshi Tanaka

2014 International Workshop on Nonlinear PDE and Applications　2014/03
２点境界値問題の正値解の対称性の破れ Invited

田中敏

松山解析セミナー 2014　2014/02
A note on the symmetry-breaking and Morse index for positive solutions of one-dimensional Henon type equations

田中敏

日本数学会2013年度秋季総合分科会　2013/09
Morse index and symmetry-breaking for positive solutions of one-dimensional Henon type equations International-presentation

Satoshi Tanaka

Equadiff 13　2013/08
Morse index and symmetry-breaking for positive solutions of one-dimensional Henon type equations International-presentation

Satoshi Tanaka

ICCM 2013　2013/07
Exact multiplicity of positive solutions for a class of two-point boundary value problems with one-dimensional p-Laplacian

田中敏

日本数学会2013年度年会　2013/03
一次元 p-Lapace 作用素をもつ２点境界値問題の正値解の厳密な個数

田中敏

振動理論ワークショップー松山 2013　2013/02
Morse indices of positive solutions for the one-dimensional Henon equation and its application to the number of positive solutions International-presentation Invited

Satoshi Tanaka

International Workshop on Stationary Problems in Nonlinear Partial Differential Equations　2013/01
Symmetry-breaking and Morse index for positive solutions of the Henon equation

田中敏

富山解析セミナー2012　2012/10
優線形２点境界値問題の正値解の非一意性 ―正値偶関数解の対称性の破れ― Invited

田中敏

日本数学会2012年度秋季総合分科会　2012/09
On the nonuniqueness of positive solutions for a class of superlinear problems International-presentation Invited

Satoshi Tanaka

The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications　2012/07
２階線形常微分方程式の振動解のフラクタル次元

田中敏

微分方程式の定性的理論ワークショップ　2012/03
Recti able and fractal oscillations of second-order linear differential equations International-presentation Invited

Satoshi Tanaka

Recti able and fractal oscillations of second-order linear differential equations　2012/02
Exact multiplicity of positive solutions for a class of two-point boundary value problems with one-dimensional p-Laplacian International-presentation Invited

Satoshi Tanaka

2012 International Workshop on Nonlinear PDE and Applications　2012/02
２階線形常微分方程式の振動解のフラクタル次元

田中敏

振動理論ワークショップー尾道 2012　2012/02
Nonuniqueness of positive solutions of two-point boundary value problems for superlinear equations International-presentation

Satoshi Tanaka

Equadiff 2011　2011/08
Rectifiable oscillations of self-adjoint and damped linear differential equations of second-order International-presentation Invited

Satoshi Tanaka

International Workshop on Geometric and fractal analysis of PDEs and differential　2011/07
On the nonuniqueness of positive solutions of two-point boundary value problems for superlinear equations International-presentation

Satoshi Tanaka

2011 International Workshop on Nonlinear PDE and Applications　2011/06
２階自己随伴型線形微分方程式の振動解の長さによる分類

田中敏

振動理論ワークショップー徳島 2011　2011/02
Emden-Fowler 型微分方程式の２点境界値問題の正値解について

田中敏

微分方程式の定性的理論ワークショップin 岡山理大　2011/01
On the nonuniqueness of positive solutions of boundary value problems for superlinear Emden-Fowler equations International-presentation Invited

Satoshi Tanaka

RIMS 研究集会新しい視点からの現象解析と関数方程式　2010/11
２階自己随伴型線形微分方程式の有限長振動と無限長振動について

田中敏

富山解析セミナー２０１０　2010/10
Uniqueness of positive radial solutions of superlinear elliptic equations in a ball International-presentation Invited

Satoshi Tanaka

The 8th AIMS International Conference on Dynamic Systems and Differential Equations　2010/05
Emden-Fowler 型微分方程式の２点境界値問題の正値解の一意性について

田中敏

日本数学会2010年度年会　2010/03
Uniqueness and nonuniqueness of positive solutions for two-point boundary value problems of Emden-Fowler equations International-presentation Invited

Satoshi Tanaka

Japan-Korea Joint Workshop on Dynamical Systems and Related Topics　2010/03
Emden-Fowler 型常微分方程式の２点境界値問題の正値解の非一意性について

田中敏

振動理論ワークショップ－倉敷 2010　2010
On the uniqueness of positive solutions of two-point BVPs of Emden-Fowler equations International-presentation Invited

Satoshi Tanaka

Second Chile-Japan Workshop on Nonlinear Elliptic and Parabolic PDE　2009/12
New sufficient conditions for the uniqueness of positive solutions of boundary value problems of Emden-Fowler equations International-presentation Invited

Satoshi Tanaka

Interenational Workshop on Qualitative Theory of ODEs in Hiroshima 2009　2009/11
Emden-Fowler 型常微分方程式の２点境界値問題の正値解の一意性について

田中敏

広島大学における微分方程式セミナー (微分方程式セミナー通算第３２回)　2009/09
On the uniqueness of positive solutions for two-point boundary value problems of Emden-Fowler differential equations International-presentation

Satoshi Tanaka

Equadiff 12　2009/07
Uniqueness of positive solutions for two-point boundary value problems of Emden-Fowler differential equations International-presentation Invited

Satoshi Tanaka

International Workshop on Nonlinear PDE and Applications　2009/06
Emden-Fowler 型常微分方程式の2点境界値問題の正値解

田中敏

微分方程式の定性的理論ワークショップ　2009/03
On the nonuniqueness of nodal radial solutions of sublinear elliptic equations in a ball

田中敏

日本数学会2009年度年会　2009/03
Emden-Fowler 型常微分方程式の２点境界値問題の正値解の個数について

田中敏

振動理論ワークショップ－松山 2009　2009/02
Uniqueness and nonuniqueness of nodal radial solutions of sublinear elliptic equations in a ball International-presentation Invited

Satoshi Tanaka

非線形偏微分方程式における定常問題　2008/12
On the uniqueness and nonuniqueness of nodal radial solutions of sublinear ellipticequations in a ball

田中敏

RIMS 研究集会関数方程式のダイナミクスと数理モデル　2008/11
On the nonuniqueness of nodal radial solutions of sublinear elliptic equations in a ball

田中敏

富山解析セミナー2008　2008/10
Nonuniqueness of nodal radial solutions of sublinear elliptic equations in a ball

田中敏

札幌医科大学における微分方程式セミナー（通算第３１回）　2008/09
An identity for BVPs with the one-dimensional p-Laplacian and its applications to the uniqueness of solutions International-presentation Invited

Satoshi Tanaka

Intensive Lecture Program and International Conference on Nonlinear PDE and Applications　2008/06
On the uniqueness of nodal radial solutions of sublinear elliptic equations in a ball International-presentation Invited

Satoshi Tanaka

The 7th AIMS International Conference on Dyn. Systems, Diff. Equations and Applications　2008/05
一階非線形遅れ型微分方程式の終局的に正の解について

田中敏

微分方程式の定性的理論ワークショップ　2008/03
一階非線形遅れ型方程式の終局的に正の解の存在と非存在

田中敏

振動理論ワークショップ－福岡 2008　2008/02
An identity for a quasilinear ordinary differential equation and its applications

田中敏

関数方程式論におけるモデリングと複素解析 (RIMS 研究集会)　2007/11
準線形常微分方程式に関するある恒等式とその応用

田中敏

富山解析セミナー2007　2007/09
準線形常微分方程式に関するある恒等式とその境界値問題への応用

田中敏

上越教育大学における微分方程式セミナー (通算第30回)　2007/08
An identity for ordinary differential equations with the one-dimensional p-Laplacian and its applications to boundary value problems International-presentation

Satoshi Tanaka

Equadiff 07　2007/08
準線形常微分方程式に関するある恒等式

田中敏

振動理論ワークショップ－岡山 2007　2007/02
On the uniqueness of nodal radial solutions of superlinear elliptic equations in a ball

田中敏

現象からの関数方程式 (RIMS 研究集会)　2006/11
On radial oscillatory solutions of a superlinear elliptic equation

田中敏

島根大学における微分方程式セミナー (通算第29回)　2006/09
Radial oscillatory solutions of a superlinear elliptic equation

田中敏

日本数学会 2006年度秋季総合分科会　2006/09
２点境界値問題の指定された個数の零点をもつ解の一意性とその楕円型方程式の球対称解への応用 Invited

田中敏

微分方程式の総合的研究　2005/12
On the uniqueness of nodal radial solutions of sublinear elliptic equations in a ball

田中敏

関数方程式の解のダイナミクスと数値シミュレーション(京都大学数理解析研究所共同研究事業)　2005/08
Multiplicity of solutions of the boundary value problem for a class of ordinary differential equations with the one-dimensional p-Laplacian

田中敏

広島大学における微分方程式セミナー（通算第２８回）　2005/08
円環領域における楕円型方程式の境界値問題の解の個数

田中敏

関数微分方程式牛窓セミナー２００５　2005/08
On the existence of solutions with prescribed numbers of zeros of two-point boundary value problems for the one-dimensional p-Laplacian International-presentation

Satoshi Tanaka

Conference on Differential & Difference Equations and Applications　2005/08
Existence of solutions with prescribed numbers of zeros of two-point boundary value problems for the one-dimensional p-Laplacian International-presentation

Satoshi Tanaka

EQUADIFF 11　2005/07
Uniqueness of nodal radial solutions of sublinear elliptic equations in a bal

田中敏

日本数学会 2005 年度年会　2005/03
On the uniqueness of nodal radial solutions of sublinear elliptic equations in a ball

田中敏

関数方程式と複雑系(京都大学数理解析研究所共同研究事業)　2005/03
ある非線形常微分方程式の２点境界値問題の解の一意性について

田中敏

愛媛大学における微分方程式セミナー (通算第 27 回)　2004/09
On the uniqueness of solutions with prescribed numbers of zeros for two-point boundary value problems

田中敏

日本数学会 2004 年度秋季総合分科会　2004/09
Uniqueness of solutions with prescribed numbers of zeros for two-point boundary value problems

田中敏

数理モデルと関数方程式の解のダイナミクス(京都大学数理解析研究所共同研究事業)　2003/11
非線型微分方程式の境界値問題の解の多重性について

田中敏

神戸大学における微分方程式セミナー (通算第 26 回)　2003/09
Multiple solutions of the boundary value problem for nonlinear second order differential equations International-presentation

Satoshi Tanaka

Toyama Conference on Differential Equations - 2003　2003/08
２階非線形常微分方程式に対する２点境界値問題の解の存在

田中敏

日本数学会 2003年度年会　2003/03
Existence of multiple solutions of the boundary value problem for nonlinear second order differential equations

田中敏

振動理論ワークショップ－富山 2003　2003/01
On the existence of solutions of the boundary value problem for nonlinear second order differential equations

田中敏

関数方程式と数理モデル(京都大学数理解析研究所共同研究事業)　2002/11
２階非線形常微分方程式に対する２点境界値問題の解の存在について

田中敏

崇城大学における微分方程式セミナー (通算第 25 回)　2002/08
Existence of solutions of two point boundary value problems with concave and convex nonlinearities

田中敏

関数方程式の解のダイナミクスとその周辺 (京都大学数理解析研究所共同研究事業)　2001/11
Existence of solutions of two point boundary value problem for second order differential equations with concave and convex nonlinearities

田中敏

広島大学における微分方程式セミナー (通算第 24 回)　2001/09
Oscillation of even order neutral differential equations

田中敏

関数方程式の定性的理論とその現象解析への応用 (京都大学数理解析研究所共同研究事業)　2000/11
Oscillation of solutions of even order neutral differential equations

田中敏

福岡大学微分方程式セミナー　2000/10
偶数階中立型関数微分方程式の振動定理

田中敏

日本数学会 2000 年度秋季総合分科会　2000/09
An oscillation theorem for a class of even order neutral differential equations

田中敏

愛媛大学における微分方程式セミナー (通算第 23 回)　2000/08
中立型関数微分方程式の解の存在と漸近挙動 Invited

田中敏

第２７回広島数理解析セミナー（２０００年）　2000/02
中立型微分方程式の振動解の存在

田中敏

日本数学会中国・四国支部例会　2000/01
A necessary and sufficient condition for the oscillation of a class of even order neutral differential equations International-presentation

田中敏

福岡大学微分方程式セミナー　1999/12
Existence of oscillatory solutions of neutral differential equations

田中敏

数理モデルと関数方程式(京都大学数理解析研究所共同研究事業)　1999/11
A comparison theorem for a certain neutral differential equation

田中敏

日本数学会 1998 年度秋季総合分科会　1999/09
偶数階中立型微分方程式の振動性

田中敏

富山大学における微分方程式セミナー (通算第 22 回)　1999/08
A comparison theorem for a class of even order neutral differential equations

田中敏

微分方程式八海山セミナー９９　1999/07
中立型微分方程式に対する比較定理

田中敏

関数方程式の方法とその応用(京都大学数理解析研究所共同研究事業)　1998/11
Existence theorems for neutral differential equations

田中敏

日本数学会 1998 年度秋季総合分科会　1998/09
中立型微分方程式の解の存在と漸近挙動

田中敏

徳島大学における微分方程式セミナー(通算第 21 回)　1998/08
Positive solutions of higher order nonlinear neutral differential equations

田中敏

微分方程式湖畔セミナー９８ in Matsue　1998/07
周期的な係数もつ一階中立型関数微分方程式の正値解

田中敏

日本数学会 1998 年度年会　1998/03
Existence of positive solutions of nonlinear functional differential equations of neutral type

田中敏

非線型微分方程式の定性的理論　1998/01
中立型微分方程式のある終局的正値解が存在するための必要十分条件

田中敏

非線形の数理と関数方程式(京都大学数理解析研究所共同研究事業)　1997/11
中立型関数微分方程式の振動解の存在について

田中敏

微分方程式関数微分方程式白州セミナー９７　1997/09
高階中立型関数微分方程式の終局的正値解の存在性

田中敏

日本数学会 1997 年度秋季総合分科会　1997/09
高階中立型関数微分方程式の終局的正値解の存在

田中敏

愛媛大学における微分方程式セミナー (通算第 20 回)　1997/08
中立型関数微分方程式の解の振動性について

田中敏

日本数学会 1997 年度年会　1997/04
一階中立型関数微分方程式の解の振動性

田中敏

日本数学会中国・四国支部例会　1997/01
二階非線形中立型関数微分方程式の解の振動性について

田中敏

愛媛大学における微分方程式セミナー (通算第 18 回)　1995/08

Show all Show first 5

Research Projects 15

境界値問題における諸種の微分作用素とラプラス作用素の効果の違いの解明

田中敏, 内藤雄基, 渡邉宏太郎, 田中視英子

Offer Organization: 日本学術振興会

System: 科学研究費助成事業

Category: 基盤研究(B)

Institution: 東北大学

2025/04/01 - 2029/03/31
Symmetry and asymmetry of solutions for the elliptic partial differential equations.

Kajikiya Ryuji

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (C)

2020/04/01 - 2024/03/31

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We consider the Moore-Nehari ordinary differential equation under the Dirichlet boundary condition in the interval (-1,1). We prove the existence of a solution which has exactly m zeros in the interval (-1,0) and exactly n zeros in (0,1) for given nonnegative integers m and n. For a non-negative integer n, we call a solution u(x) n-nodal if it has exactly n zeros in (-1,1). We call a solution symmetric if it is even or odd. For each n, the equation has a unique n-nodal symmetric solution, which is a continuous curve. We prove that the curve bifurcates and an asymmetric solution emanates.
Nonlinear Elliptic Equations and Its Applications

2022/04 - 2024/03
２点境界値問題の解の厳密な個数と分岐現象

田中敏

Offer Organization: 日本学術振興会

System: 科学研究費助成事業基盤研究(C)

Category: 基盤研究(C)

Institution: 岡山理科大学

2019/04/01 - 2022/03/31
Analysis of singular nonlinear structure in dissipative systems

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (A)

Category: Grant-in-Aid for Scientific Research (A)

Institution: Tokyo Institute of Technology

2017/04/01 - 2022/03/31
International Workshop on Nonlinear Elliptic Equations and Its Applications

2020/04 - 2022/03
The number of solutions and the length and the fractal dimension of oscillatory solutions of two point boundary problems Competitive

Tanaka Satoshi, Onitsuka Masakazu, Naito Yuki, Kajikiya Ryuji, Tanaka Mieko, Kanemitsu Takanao, Shioji Naoki, Watanabe Kohtaro, Pasic Mervan, Sim Inbo, Wu Fentao, Wang Shin-Hwa, Hung Kuo-Chih, Manasevich Raul, Garcia-Huidobro Marta

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

Category: Grant-in-Aid for Scientific Research (C)

Institution: Okayama University of Science

2014/04/01 - 2019/03/31

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The number of solutions and the length and the fractal dimension of oscillatory solutions of two point boundary problems are studied, and then the following results were established. Sufficient conditions for the existence of three positive solutions to two point boundary problem with a sign-changing weight function and the one-dimensional p-Lalpacian were obtained. Results on the number of solutions to the autonomous two point boundary problem with (p,q)-Lalpacian were obtained. The symmetry-breaking bifurcations for the one-dimensional Liouville type equation and the one-dimensional Henon equation were found. Results on the non-rectifiability and the box-counting dimension of solution curves of two-dimensional non-autonomous linear and half-linear differential systems were obtained.
The number of nonoscillatory solutions and the length and the fractal dimension for two-point boundary value problems

TANAKA Satoshi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)

Category: Grant-in-Aid for Young Scientists (B)

Institution: Okayama University of Science

2011 - 2013

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In this study, two-point boundary value problems for nonlinear ordinary differential equations were considered. The positive solution is a kind of nonoscillatory solutions. The symmetry-breaking for positive solutions was proved by finding the Morse index of positive solutions. Then the existence of positive symmetry solutions and positive asymmetry solutions was shown, and therefore, a result of the nonuniqueness of positive solutions was established. A sufficient condition is obtained for the existence of exact two positive solutions of problems with one dimensional p-Laplacian. The fractal dimension of radial oscillatory solutions for a class of elliptic partial differential equations was found.
Study of the solution semigroup for integral equations and related topics

MURAKAMI Satoru, HAMAYA Yoshihiro, NAGABUCHI Yutaka, KAMIYA Shigeyasu, TANAKA Satoshi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

Category: Grant-in-Aid for Scientific Research (C)

Institution: Okayama University of Science

2010 - 2012

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We studied some qualitative properties of solutions in integral equations. Indeed, for linear integral equations we analyzed some spectral properties for the generator of the associated solution semigroup, and obtained an estimate on the essential spectral radius of the generator. Furthermore, we established a representation formula in the phase space for solutions of nonhomogeneous linear equations. Applying these results, we obtained Massera type results on the existence of bounded solutions, periodic solutions and so on. Also, for nonlinear integral equations we established the principle of linearization which is effectively applicable to stability problems in nonlinear equations.
A study on the number of sign-changing solutions of two-point boundary value problems and its application

TANAKA Satoshi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)

Category: Grant-in-Aid for Young Scientists (B)

Institution: Okayama University of Science

2008 - 2010

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In this study, two-point boundary value problems for nonlinear ordinary differential equations are considered. New results for the uniqueness of sign-changing solutions are established. As its application we have obtained sufficient conditions for the uniqueness of sign-changing radial solutions of boundary value problems of elliptic partial differential equations in a ball. Moreover the nonuniqueness examples for sign-changing radial solutions are also given. It is expected that we can obtain exact multiplicity results for sign-changing solutions of two-point boundary value problems by applying the method used here.
Study of stability properties for positive linear equations with delay and related topics

MURAKAMI Satoru, KAMIYA Shigeyasu, HAMAYA Yoshihiro, NAGABUCHI Yutaka, TANAKA Satoshi, SHIMENO Nobukazu

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

Category: Grant-in-Aid for Scientific Research (C)

Institution: Okayama University of Science

2007 - 2009

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We studied qualitative properties of solutions in functional differential equations, integrodifferential equations and Volterra difference equations which are typical ones of equations with delay. Applying the variation-of-constants formula in the phase space for functional differential equations, we obtained a result on the behavior of solutions for equations with a perturbation. Also, we established a result on the existence of several invariant manifolds for nonlinear functional differential equations. Furthermore, treating integrodifferential equations mainly, we investigated the positivity of equations, and obtained a criterion on stabilities for positive equations.
Oscillation theory and singular boundary value problems for higher-order ordinary differential equations

NAITO Manabu, SUGIE Jitsuro, USAMI Hiroyuki, TANAKA Satoshi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

Category: Grant-in-Aid for Scientific Research (C)

Institution: Ehime University

2007 - 2008
Self-similar structure and singularity of solutions for nonlinear parabolic partial differential equations

NAITO Yuki, ISHI Katsuyuki, KUWAMURA Masataka, SUZUKI Takashi, SATO Tokushi, TANAKA Satoshi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

Category: Grant-in-Aid for Scientific Research (C)

Institution: Kobe University

2005 - 2007

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Structure of self-similar solutions for nonlinear parabolic partial differential equations and the role of self-similar solutions for the asymptotic behavior of time-global solutions and the finite time blow up solutions are studied. In particular, we consider the structure of self-similar solutions for semilinear heat equations, the role of self-similar solutions in the blow-up phenomena for nonlinear heat equations, and the structure of self-similar solutions for chemotaxis system. We show the multiple existence of positive self-similar solutions for semilinear heat equations with sub-critical and critical nonlinearity by employing variationa methods for semilinear elliptic partial differential equations. In the super-critical case, we show the existence and some properties of positive self-similar solutions by using of the ordinary differential methods. We show some criterion for blow up rate of solutions of semilinear heat equations with critical Sobolev nonlinearity. In particular we verify that a solution must blow up in the self-similar rate, which is called type-I blow up rate, if the solution is positive on the backward parbolic space-time region. In addition, we show, in the case where space dimension is 3, there exist solutions which blow up in specific blow-up rate, called type II blow up rate, when the domain shrinks with suitable rate. We show that time-global solutions for parabolic chemotaxis system asymptotic to forward self-similar solutions as time gtends to the infinity in the case where space dimensional is 2. We also show the non-existence of backward self-similar solutions for chemotaxis system in the 2-dimensional case. We consider the representation of positive solutions for semilinear elliptic equations with singular forcing terms, and then, we show the existence of positive minimal solution and the second positive solutions.
Formal adjoint equation for equations with time delay and its applications

MURAKAMI Satoru, KAMIYA Shigeyasu, HAMAYA Yoshihiro, SHIMENO Nobukazu, NAGABUCHI Yutaka, TANAKA Satoshi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

Category: Grant-in-Aid for Scientific Research (C)

Institution: Okayama University of Science

2004 - 2006

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Head investigator and five investigators studied qualitative properties of solutions of functional differential equations, integrodifferential equations and Volterra difference equations which are typical ones of equations with delay, and obtained many results on the subject as cited below. 1. For linear integrodifferential equations with integrable kernels, we characterized uniform asymptotic stability property of the zero solution in terms of the distribution of spectrum of the characteristic operator as wellas the integrability of the resolvent. As an application of the result, for equations with almost periodic perturbation we obtained a sufficient condition for the existence of almost periodic solutions, and analyzed the spectrum of the almost periodic solutions. Furthermore, applying the method to Volterra difference equations, we obtained some result on the stability property of the solution of partial differential equations with piecewise continuous delay. 2. Using a variation-of-constants formula in the phase space for linear equations with delay, we established the existence of invariant manifolds (such as local stable manifold, local center manifold and so on) for some nonlinear equations, and applied the result to the stability problem. Also, through some finer considerations, we investigated the smoothness of the invariant manifolds. 3. For linear functional difference equations with perturbations, we investigated the asymptotic behavior of solutions by decomposing the phase space into the direct sum of the stable subspace and the unstable manifold by means of the spectrum analysis of the solution operator, and obtained an extension of the Perron theorem for ordinary differential equations.
漸近挙動による中立型微分方程式の正値解の分類とその構造に関する研究

田中敏

Offer Organization: 日本学術振興会

System: 科学研究費助成事業若手研究(B)

Category: 若手研究(B)

2002 - 2004

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本研究に関係することが期待されている、ある種の境界値問題の解の一意性についてこれまでの研究でわかったことを「愛媛大学における微分方程式セミナー」や「日本数学会2004年度秋季総合分科会」で講演発表した。また、今年度は内藤助教授(神戸大学)との共著論文「On the existence of multiple solutions of the boundary value problem for nonlinear second order differential」が学術雑誌「Nonlinear Analysis」に発表された。さらに、2つの論文が掲載受理された。1つは、雑誌「Annales Polonici Mathematici」に受理された吉田教授(富山大学)との共著「Forced Oscillation of Certain Hyperbolic Equations with Continuous Distributed Deviating Arguments」である。この論文ではある双曲型の偏微分方程式の問題を常微分中立型微分不等式に帰着することにより、双曲型の問題のすべての解が振動である十分条件を得た。もう1つは「Mathematics Journal of Toyama University」に受理された「Oscillation criteria for a class of second order forced neutral differential equations」である。この論文ではある2階の中立型微分方程式のすべての解が振動であるための十分条件を得ている。その結果は過去のいくつかの結果の拡張になっている。中立型微分方程式には様々な正値解が存在することが過去の結果により知られているが、それらの結果を拡張し、さらに、統一的にまとめることができることができた。それらの結果をまとめた論文が現在投稿中である。

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