Existence of solutions for asymptotically periodic fractional Schrödinger equation

In this paper we study the following nonlinear fractional Schrödinger equation (−Δ)su+V(x)u=f(x,u),x∈RN,where s∈(0,1), (−Δ)s is the fractional Laplacian operator of order s, and V, f are asymptotically periodic functions in x. Under suitable conditions, the existence of nontrivial solution is obtained by using variational methods and concentration compactness argument.