Ground state solutions of asymptotically linear fractional Schrödinger equations

Abstract

This paper is devoted to a time-independent fractional Schrödinger equation of the form \documentclass[12pt]{minimal}\begin{document}$(-\Delta )^s u+V(x)u=f(x,u)\; \mbox{in}\; \mathbb {R}^{N},$\end{document}(−Δ)su+V(x)u=f(x,u)inRN, where N ⩾ 2, s ∈ (0, 1), (−Δ)s stands for the fractional Laplacian. We apply the variational methods to obtain the existence of ground state solutions when f(x, u) is asymptotically linear with respect to u at infinity.