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

Abstract

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.