On fractional Schrodinger equation with periodic and asymptotically periodic conditions

In this paper, we study the following fractional Schrodinger equation (-Delta)(s)u + V(x)u = f(x,u), x is an element of R-N, where ( -Delta)(s)(s is an element of (0, 1)) denotes the fractional Laplacian. Under some weaker conditions on the nonlinearity, we obtain the existence of solutions for the above problem in periodic case and asymptotically periodic case via variational methods, respectively. (C) 2017 Elsevier Ltd. All rights reserved.