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2008 Fiscal Year Self-evaluation Report

On the multiplicity and dynamics of solutions of nonlinear Differential equations

Research Project

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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)

Project Period (FY) 2006 – 2009
Keywords変分法 / 非線形微分方程式 / カオス
Research Abstract

(1) 非線形楕円型境界値問題の解の多重性と定義域の関係の解明 : 非線形楕円型境界値問題において方程式の定義域の位相的、幾何学的特徴が微分方程式の解の多重性に与える影響を明らかにする。
(2) 非有界な領域で定義された楕円型, 及び放物型偏微分方程式の解の多重性と特性の解明:定義域が非有界な楕円型及び放物型の方程式は, 定義域が有界な場合の方程式と方程式自体の形が同じであっても別の手法が必要である。このような方程式の解の存在を明らかにする。
(3) 遅れを持つ微分方程式の解の存在及び多重性の研究 : ロジスティック方程式や, ロトカ-ボルテラ方程式のような常微分方程式のシステムに時間的遅れがある場合の解の存在、性質を明らかにする。

  • Research Products

    (6 results)

All 2009 2008

All Journal Article (6 results)

  • [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

  • [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

  • [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

  • [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

  • [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

  • [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

URL: 

Published: 2010-06-11   Modified: 2016-04-21  

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