On fractional Schrödinger 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 Schrödinger equations in $\mathbb{R}^N$ of the form \begin{equation*} (-\Delta)^s u + V(x) u = g(u), \end{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.