The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function

K. J. Brown, Yanping Zhang

Research output: Contribution to journalArticle

251 Citations (Scopus)

Abstract

The Nehari manifold for the equation -?u(x) = ?a(x)u(x) + b(x) u(x)v-1u(x) for x?O together with Dirichlet boundary conditions is investigated. Exploiting the relationship between the Nehari manifold and fibrering maps (i.e., maps of the form t ? J(tu) where J is the Euler functional associated with the equation) we discuss how the Nehari manifold changes as ? changes and show how existence and non-existence results for positive solutions of the equation are linked to properties of the manifold. © 2003 Elsevier Science (USA). All rights reserved.

Original languageEnglish
Pages (from-to)481-499
Number of pages19
JournalJournal of Differential Equations
Volume193
Issue number2
DOIs
Publication statusPublished - 20 Sep 2003

Keywords

  • Indefinite weight functions
  • Nehari manifold
  • Variational methods

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