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A positive solution for an asymptotically linear elliptic problem on $\Bbb R^{N}$ autonomous at infinity. (English) Zbl 1225.35088
Summary: We establish the existence of a positive solution for an asymptotically linear elliptic problem on $\Bbb R^N$. The main difficulties 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.

MSC:
35J60Nonlinear elliptic equations
58E05Abstract critical point theory
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References:
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