Existence of solutions for fractional Schrodinger equation with asymptotically periodic terms

In this paper, we investigate the following nonlinear fractional Schrodinger equation (−∆) ^su + V(x)u = f(x, u), x ∈ R^N,where s ∈ (0, 1), N 2 and (−∆)^s is fractional Laplacian operator. We prove that the problem has a non-trivial solution under asymptotically periodic case of V and f at infinity. Moreover, the nonlinear term f does not satisfy any monotone condition and Ambrosetti-Rabinowitz condition