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arXiv:1210.0755 [math.AP]AbstractReferencesReviewsResources

On fractional Schrödinger equations in (\mathbb{R}^N) without the Ambrosetti-Rabinowitz condition

Simone Secchi

Published 2012-10-02, updated 2014-02-11Version 2

In this note we prove the existence of radially symmetric solutions for a class of fractional Schr\"odinger equation in (\mathbb{R}^N) of the form {equation*} \slap u + V(x) u = g(u), {equation*} where the nonlinearity $g$ does not satisfy the usual Ambrosetti-Rabinowitz condition. Our approach is variational in nature, and leans on a Pohozaev identity for the fractional laplacian.

Comments: 26 pages. To appear on Topological Methods In Nonlinear Analysis
Categories: math.AP
Subjects: 35Q55, 35A15, 35J20
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