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.
|ジャーナル||ESAIM - Control, Optimisation and Calculus of Variations|
|出版ステータス||Published - 2002 8|
ASJC Scopus subject areas
- Control and Systems Engineering
- Control and Optimization
- Computational Mathematics