Existence of nodal solutions for quasilinear elliptic problems in $R^N$

Ann Derlet, Francois Genoud

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We prove the existence of one positive, one negative and one sign-changing solution of a p-Laplacian equation on ℝN with a p-superlinear subcritical term. Sign-changing solutions of quasilinear elliptic equations set on the whole of ℝN have scarcely been investigated in the literature. Our assumptions here are similar to those previously used by some authors in bounded domains, and our proof uses fairly elementary critical point theory, based on constraint minimization on the nodal Nehari set. The lack of compactness due to the unbounded domain is overcome by working in a suitable weighted Sobolev space
Original languageEnglish
Pages (from-to)937-957
Number of pages21
JournalRoyal Society of Edinburgh. Proceedings. Section A(Mathematics)
Volume145
Issue number5
DOIs
Publication statusPublished - 24 Aug 2015

Keywords

  • quasilinear elliptic equations
  • unbounded domain
  • sign-changing solutions
  • Nehari manifold
  • weighted Sobolev spaces

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