On the existence of multiple solutions of the boundary value problem for nonlinear second-order differential equations

Yuki Naito, Satoshi Tanaka

Research output: Contribution to journalArticle

57 Citations (Scopus)

Abstract

We consider the boundary value problem for nonlinear second-order differential equations of the form u″ + a(x)f(u) = 0, 0 < x < 1, u(0) = u(1) = 0. We establish the precise condition concerning the behavior of the ratio f(s)/s at infinity and zero for the existence of solutions with prescribed nodal properties. Then we derive the existence and the multiplicity of nodal solutions to the problem. Our argument is based on the shooting method together with the Strum's comparison theorem. The results obtained here can be applied to the study of radially symmetric solutions of the Dirichlet problem for semilinear elliptic equations in annular domains.

Original languageEnglish
Pages (from-to)919-935
Number of pages17
JournalNonlinear Analysis, Theory, Methods and Applications
Volume56
Issue number6
DOIs
Publication statusPublished - 2004 Mar 1
Externally publishedYes

Keywords

  • Shooting method
  • Two-point BVP

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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