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A positive solution for an asymptotically linear elliptic problem on $\mathbb{R}^N$
autonomous at infinity
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- Journal:
- ESAIM: Control, Optimisation and Calculus of Variations / Volume 7 / 2002
- Published online by Cambridge University Press:
- 15 September 2002, pp. 597-614
- Print publication:
- 2002
-
- Article
- Export citation
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In this paper we establish the existence of a positive solutionfor an asymptotically linear elliptic problem on $\xR^N$
. The maindifficulties to overcome are the lack of a priori bounds forPalais–Smale sequences and a lack of compactness as the domain isunbounded. For the first one we make use of techniques introducedby Lions in his work on concentration compactness. For thesecond we show how the fact that the “Problem at infinity” isautonomous, in contrast to just periodic, can be used in order toregain compactness.
