Multiple solutions of nonlinear Schrodinger equation with the fractional Laplacian

In this paper we are devoted to a time-independent fractional Schrodinger equation (-Delta)(alpha)u + V(x)u = f (x, u) in R-N, where (-Delta)(alpha) stands for the fractional Laplacian of order alpha is an element of (0, 1), f is either asymptotically linear or superquadratic growth. Under appropriate assumptions on V and f, we prove the existence of infinitely many nontrivial high or small energy solutions, which extend and complement previously known results in the literature. (C) 2016 Elsevier Ltd. All rights reserved.