A positive solution for an asymptotically linear elliptic problem on ℝn autonomous at infinity

Louis Jeanjean, Kazunaga Tanaka

Research output: Contribution to journalArticle

93 Citations (Scopus)

Abstract

In this paper we establish the existence of a positive solution for an asymptotically linear elliptic problem on ℝn. The main diffculties to overcome are the lack of a priori bounds for Palais-Smale sequences and a lack of compactness as the domain is unbounded. For the first one we make use of techniques introduced by Lions in his work on concentration compactness. For the second we show how the fact that the “Problem at infinity” is autonomous, in contrast to just periodic, can be used in order to regain compactness.

Original languageEnglish
Pages (from-to)597-614
Number of pages18
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume7
DOIs
Publication statusPublished - 2002 Aug

Keywords

  • Asymptotically linear problems in ℝ
  • Elliptic equations
  • Lack of compactness

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics

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