Profile and multiplicity of solutions of nonlinear differential equations

• Project/Area Number: 22540177
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Yokohama National University
• Principal Investigator: HIRANO Norimichi 横浜国立大学, 環境情報研究院, 教授 (80134815)
• Project Period (FY): 2010-04-01 – 2014-03-31
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 解の多重性 / カオス / 非線形微分方程式 / 変分法 / 多重解 / homoclinic solution / シュレジンガー方程式

Research Abstract

In this research, I investigated the existence and multiplicity of the solutions of nonlinear elliptic problems defined on domains which have holes, and showed some properties of solutions. On the other hand, we established the existence of solutions of nonlinear Schrodinger equations defined on Reimannian manifolds and showed the relation between the Ricci curvature and the multiplicity of solutions.

Research Products

• [Journal Article] Bifurcations of nonconstant solutions of the Ginzburg-Landau equation (2012)
  • Author(s): Hirano, Norimichi; Rybicki, Sławomir
  • Journal Title: Abstr. Appl. Anal. Pages: 19-19
  • Peer Reviewed
• [Journal Article] Multiple existence of solutions for a singularly perturbed nonlinear elliptic problem on a Riemannian manifold (2012)
  • Author(s): Hirano, Norimichi
  • Journal Title: Proc. Roy. Soc. Edinburgh Sect. A Volume: 142, no.1 Pages: 81-114
  • Peer Reviewed
• [Journal Article] Bifurcations of nonconstant solutions of the Ginzburg-Landau equation (2012)
  • Author(s): Hirano, Norimichi
  • Journal Title: Abstr. Appl. Anal Volume: 19 Pages: 213-225
  • Peer Reviewed
• [Journal Article] Multiple existence of solutions for a singularly perturbed nonlinear elliptic problem on a Riemannian manifold (2012)
  • Author(s): Hirano, Norimichi
  • Journal Title: .Proc. Roy. Soc. Edinburgh Sect. A Volume: 142 Pages: 81-114
  • Peer Reviewed
• [Journal Article] Existence of two solutions for the Bahri-Coron problem in an annular domain with a thin hole (2011)
  • Author(s): Hirano, Norimichi; Shioji, Naoki
  • Journal Title: J. Funct. Anal. Volume: 261, no.12 Pages: 3612-3632
  • Peer Reviewed
• [Journal Article] A remark on global bifurcations of solutions of Ginzburg-Landau equation (2011)
  • Author(s): Hirano, Norimichi; Rybicki, Sławomir
  • Journal Title: Nonlinear Anal. Real World Appl. Volume: 12, no.6 Pages: 2943-2946
  • Peer Reviewed
• [Journal Article] Se Multiple existence of solutions for a nonhomogeneous elliptic problem on RN (2011)
  • Author(s): Hirano, Norimichi; Kim, Wan
  • Journal Title: Nonlinear Anal. Volume: 74, no.13 Pages: 4369-4378
  • Peer Reviewed
• [Journal Article] Existence of nonstationary periodic solutions forΓ-symmetric Lotka-Volterra type systems (2011)
  • Author(s): Hirano, Norimichi; Krawcewicz, Wieslaw; Ruan, Haibo
  • Journal Title: Discrete Contin. Dyn. Syst. Volume: 30, no.3 Pages: 709-735
  • Peer Reviewed
• [Journal Article] Multiple existence of solutions for a nonhomogeneous elliptic problem on $￥Bbb R￥sp N$RN (2011)
  • Author(s): Hirano, Norimichi
  • Journal Title: Nonlinear Anal. Volume: 74 Pages: 4369-4378
  • Peer Reviewed
• [Journal Article] A remark on global bifurcations of solutions of Ginzburg-Landau equation (2011)
  • Author(s): Hirano, Norimichi
  • Journal Title: Real World Appl. Volume: 12 Pages: 2943-2946
  • Peer Reviewed
• [Journal Article] Existence of homoclinic solutions for a nonlinear elliptic boundary value problem (2010)
  • Author(s): Amaishi, Toshiro; Hirano, Norimichi
  • Journal Title: Yokohama Math. J. Volume: 56, no.1-2 Pages: 9-30
  • Peer Reviewed
• [Journal Article] Existence of nonstationary periodic solutions for $\Gamma$Γ-symmetric Lotka-Volterra type systems (2010)
  • Author(s): Hirano, Norimichi, Krawcewicz, Wieslaw; Ruan, Haibo
  • Journal Title: Discrete Contin.Dyn.Syst. Volume: 30 Pages: 709-735
  • Peer Reviewed