A sign-changing solution for a superlinear dirichlet problem

Alfonso Castro, Jorge Cossio, John M. Neuberger

Research output: Contribution to journalArticle

181 Scopus citations

Abstract

We show that a superlinear boundary value problem has at least three nontrivial solutions. A pair are of one sign (positive and negative, respectively), and the third solution changes sign exactly once. The critical level of the sign-changing solution is bounded below by the sum of the two lesser levels of the one-sign solutions. If nondegenerate, the one sign solutions are of Morse index 1 and the signchanging solution has Morse index 2. Our results extend and complement those of Z.Q. Wang [12]

Original languageEnglish (US)
Pages (from-to)1041-1053
Number of pages13
JournalRocky Mountain Journal of Mathematics
Volume27
Issue number4
DOIs
StatePublished - Jan 1 1997

Keywords

  • Deformation lemma
  • Dirichlet problem
  • Sign-changing solution
  • Subcritical
  • Superlinear

ASJC Scopus subject areas

  • Mathematics(all)

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