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

Louis Jeanjean, Kazunaga Tanaka

研究成果: Article査読

95 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)597-614
ページ数18
ジャーナルESAIM - Control, Optimisation and Calculus of Variations
7
DOI
出版ステータスPublished - 2002 8

ASJC Scopus subject areas

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

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