Sharp conditions for the existence of sign-changing solutions to equations involving the one-dimensional p-Laplacian

Yuki Naito, Satoshi Tanaka

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

Abstract

We consider the boundary value problem involving the one-dimensional p-Laplacian (| u |p - 2 u) + a (x) f (u) = 0, 0 < x < 1, u (0) = u (1) = 0, where p > 1. We establish sharp conditions for the existence of solutions with prescribed numbers of zeros in terms of the ratio f (s) / sp - 1 at infinity and zero. Our argument is based on the shooting method together with the qualitative theory for half-linear differential equations.

Original languageEnglish
Pages (from-to)3070-3083
Number of pages14
JournalNonlinear Analysis, Theory, Methods and Applications
Volume69
Issue number9
DOIs
Publication statusPublished - 2008 Nov 1
Externally publishedYes

Keywords

  • Half-linear differential equations
  • One-dimensional p-Laplacian
  • Shooting method
  • Two-point boundary value problems

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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