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Multiplcitiy and Dynamics of solutions of nonlinear differential equations

Research Project

Project/Area Number 18540163
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionYokohama National University

Principal Investigator

HIRANO Norimichi  Yokohama National University, 環境情報研究院, 教授 (80134815)

Co-Investigator(Kenkyū-buntansha) SHIOJI Naoki  横浜国立大学, 環境情報研究院, 准教授 (50215943)
TAMANO Kenichi  横浜国立大学, 工学研究院, 教授 (90171892)
NAITO Koichiro  熊本大学, 工学部, 教授 (10164104)
KOMIYA Hidetoshi  慶応大学, 商学部, 教授 (90153676)
Project Period (FY) 2006 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,630,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥630,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
Keywords変分法 / カオス / 位相的アプローチ / 解の多重性 / 解のプロファイル / 非線形楕円型方程式 / 非線形微分方程式 / homoclinic solution / Lotoka-Volterra / Dirichlet condition / homology / sign changing solution / elleptic problem
Research Abstract

楕円型方程式のうち、非線形シュレジンガー方程式およびHennon方程式に対して、解の多重性と解のプロフィールを示すことができた。また、シンメトリーを持つような方程式を扱うための道具として、Equivariant degreeの理論の深化に成果をあげた。

Report

(6 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (31 results)

All 2009 2008 2007 2006

All Journal Article (31 results) (of which Peer Reviewed: 15 results)

  • [Journal Article] Existence of positive solutions for the Henon equation involving critical Sobolev terms2009

    • Author(s)
      Hirano, Norimichi
    • Journal Title

      J. Differential Equations 247,no.5

      Pages: 1311-1333

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Multiple existence of nonradial positive solutions for a coupled nonlinear Schrodinger system.2009

    • Author(s)
      Hirano, Norimichi
    • Journal Title

      NoDEA Nonlinear Differential Equations Appl 16,no.2

      Pages: 159-188

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Multiple existence of solutions for a nonlinear elliptic problem on a Riemannian manifold.2009

    • Author(s)
      Hirano, Norimichi
    • Journal Title

      Nonlinear Anal. 70,no.2

      Pages: 671-692

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Multiple existence of solutions for a nonlinear elliptic problem on a Riemannian manifold2009

    • Author(s)
      Hirano, N
    • Journal Title

      Nonlinear Anal. 70

      Pages: 671-692

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multiple existence of nonradial positive solutions for a coupled nonlinear Schrodinger system2009

    • Author(s)
      Hirano, N
    • Journal Title

      NoDEA Nonlinear Differential Equations Appl. 16

      Pages: 159-188

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence of Positive Solutions for The Henon Equation involving Critical Sobolev Terms2009

    • Author(s)
      Hirano, N
    • Journal Title

      J.Differential Equations 247

      Pages: 1311-1333

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multiple existence of solutions for a nonlinear elliptic problem on a Riemannian manifold2009

    • Author(s)
      Hirano, Norimichi
    • Journal Title

      Nonlinear Anal 70

      Pages: 671-692

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Multiple existence of solutions for a nonlinear elliptic problem on a Riemannian manifold2009

    • Author(s)
      Hirano, Norimichi
    • Journal Title

      Nonlinear Anal. 70

      Pages: 671-692

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Existence of multiple positive solutions for a nonlinear elliptic problem with the critical exponent and a Hardy term.2008

    • Author(s)
      Hirano, Norimichi ; Shioji, Naoki
    • Journal Title

      Differential Integral Equatons 21,no.9-10

      Pages: 971-980

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Existence of non-positive solutions for a nonhomogeneous elliptic problem on $\Bbb R\sp N$.2008

    • Author(s)
      Hirano, Norimichi; Micheletti, Anna Maria; Pistoia, Angela
    • Journal Title

      J. Nonlinear Convex Anal. 9,no.9-10

      Pages: 309-329

    • Related Report
      2009 Final Research Report
  • [Journal Article] Brezis-Nirenberg type theorems and multiplicity of positive solutions for a singular elliptic problem.2008

    • Author(s)
      Hirano, Norimichi ; Saccon, Claudio ; Shioji, Naoki
    • Journal Title

      J. Differential Equations 245,no.8

      Pages: 1997-2037

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Multiple existence of sign changing solutions for a nonlinear elliptic problem.2008

    • Author(s)
      Hirano, Norimichi
    • Journal Title

      Nonlinear Anal 68,no.5

      Pages: 1043-1063

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Angela Existence of multiple positive solutions for a nonlinear elliptic problem with the critical exponent and a Hardy term2008

    • Author(s)
      Hirano, Norimichi, Shioji, Naoki
    • Journal Title

      Differential Integral Equations 21, no.9-10

      Pages: 971-980

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Angela Existence of non-positive solutions for a nonhomogeneous elliptic problem on $\Bbb R\sp N$2008

    • Author(s)
      Hirano, Norimichi, Micheletti, Anna Maria, Pistoia
    • Journal Title

      J. Nonlinear Convex Anal 9, no.3

      Pages: 309-329

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Naoki Brezis-Nirenberg type theorems and multiplicity of positive solutions for a singular elliptic problem2008

    • Author(s)
      Hirano, Norimichi, Saccon, Claudio, Shioji
    • Journal Title

      J. Differential Equations 245, no.8

      Pages: 1997-2037

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Multiple existence of solutions for coupled nonlinear Schrodinger equations2008

    • Author(s)
      Hirano, Norimichi, Shioji, Naoki
    • Journal Title

      Nonlinear Anal 68, no.12

      Pages: 3845-3859

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Multiple existence of sign changing solutions for a nonlinear elliptic problem2008

    • Author(s)
      Hirano, Norimichi
    • Journal Title

      Nonlinear Anal 68, no.5

      Pages: 1043-1063

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Existence of non-positive solutions for a nonhomogeneous elliptic problem on $\Bbb R\sp N$2008

    • Author(s)
      Hirano, Norimichi, Micheletti, Anna Maria, Pistoia, Angela
    • Journal Title

      J. Nonlinear Convex Anal. 9

      Pages: 309-329

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Brezis-Nirenberg type theorems and multiplicity of positive solutions for a singular elliptic problem2008

    • Author(s)
      Hirano, Norimichim, Saccon, Claudio, Shioji, Naoki
    • Journal Title

      J. Differential Equations 245

      Pages: 1997-2037

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Multiple existence of solutions for coupled nonlinear Schrodinger equations2008

    • Author(s)
      Hirano, Norimichi, Shioji, Naoki
    • Journal Title

      Nonlinear Anal. 68

      Pages: 3845-3859

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Multiple existence of sign changing solutions for a nonlinear elliptic problem2008

    • Author(s)
      Hirano, Norimichi
    • Journal Title

      Nonlinear Anal. 68

      Pages: 1043-1063

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Existence of multiple positive solutions for a nonlinear elliptic problem with the critical exponent and a Hardy term2008

    • Author(s)
      Hirano, Norimichi, Shioji, Naoki
    • Journal Title

      Differential Integral Equations 21

      Pages: 971-980

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Multiple existence of sign changing solutions for a nonlinear elliptic problem2008

    • Author(s)
      Norimichi Hirano
    • Journal Title

      Nonlinear Analysis 68

      Pages: 1043-1063

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence of sign-changing solutions for a nonlinear elliptic problem on R^N with a Hardy term2008

    • Author(s)
      Norimichi Hirano
    • Journal Title

      J. Math. Anal. Appl. 339

      Pages: 1243-1252

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A multiplicity result including a sign-changing solution for an inhomogeneous Neumann problem with critical exponent.2007

    • Author(s)
      Hirano, Norimichi ; Shioji, Naoki
    • Journal Title

      Proc. Roy. Soc. Edinburgh Sect. A137,no.5

      Pages: 333-347

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A multiplicity result including sign-changing solutions for a nonlinear elliptic problem in $\bold R\sp N$.2007

    • Author(s)
      Hirano, Norimichi ; Shioji, Naoki
    • Journal Title

      Adv. Nonlinear Stud 7,no.5

      Pages: 513-532

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Multiple existence of solutions-for a nonhomogeneous elliptic problem on R^N.2007

    • Author(s)
      Norimichi Hirano
    • Journal Title

      J. Math. Anal. Appl 336

      Pages: 506-522

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multiple existence of solutions for a nonhomogeneous elliptic problem with critical exponent on $\Bbb R\sp N$.2006

    • Author(s)
      Hirano, N. ; Micheletti, Anna Maria ; Pistoia, Angela
    • Journal Title

      Nonlinear Anal 65,no.3

      Pages: 501-513

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Existence of periodic solutions for the Lotka-Volterra type systems.2006

    • Author(s)
      Hirano, N, Rybicki, S
    • Journal Title

      J.Differential Equations 229,no.1

      Pages: 121-137

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Multiple existence of solutions for a nonhomogeneous elliptic problem with critical exponent on R^N.2006

    • Author(s)
      Hirano, N, Micheletti, Anna, Maria, Pistoia, Angela
    • Journal Title

      Nonlinear Analysis. 65,no.3

      Pages: 502-513

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Existence of positive solutions for a semilinear elliptic problem with critical Sobolev and Hardy terms2006

    • Author(s)
      Hirano, N, Shioji, N
    • Journal Title

      Proc.Amer.Math.Soc. 134,no.9

      Pages: 2583-2592

    • Related Report
      2006 Annual Research Report

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Published: 2006-04-01   Modified: 2016-04-21  

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