On fractional Schrödinger equation with periodic and asymptotically periodic conditions

In this paper, we study the following fractional Schrödinger equation (−Δ)su+V(x)u=f(x,u),x∈RN,where (−Δ)s(s∈(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.