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arXiv · 1210.0755

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

Simone Secchi
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Abstract

In this note we prove the existence of radially symmetric solutions for a class of fractional Schrödinger 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.

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Simone Secchi. 2014-02-11. On fractional Schrödinger equations in (\mathbb{R}^N) without the Ambrosetti-Rabinowitz condition. https://arxiv.org/abs/1210.0755

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