On a variational problem with lack of compactness: the topological effect of the critical points at infinity

Abbas Bahri, Yanyan Li, Olivier Rey

Research output: Contribution to journalArticlepeer-review

188 Scopus citations

Abstract

We study the subcritical problems Pe{open}:-Δu=up-e{open}, u>0 on Ω;u=0 on ∂Ω, ω being a smooth and bounded domain in ℝN, N-3, p+1=2N/N-2 the critical Sobolev exponent and e{open}>0 going to zero - in order to compute the difference of topology that the critical points at infinity induce between the level sets of the functional corresponding to the limit case (P0).

Original languageEnglish (US)
Pages (from-to)67-93
Number of pages27
JournalCalculus of Variations and Partial Differential Equations
Volume3
Issue number1
DOIs
StatePublished - Jan 1995

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Keywords

  • Mathematics subject classification: 35J65

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