Solutions of nonlinear Schrödinger equation with fractional Laplacian without the Ambrosetti-Rabinowitz condition

This paper is concerned with the existence of two nonnegative radial solutions of following nonlinear Schrödinger equation with fractional Laplacian(-Δ)αu+u=f(u)inRN,u∈Hα(RN),where 0<α<1. Under certain assumptions, we obtain that the above problem has at least two nontrivial radial solutions without assuming the Ambrosetti-Rabinowitz condition by variational methods and concentration compactness principle. The result extends one of the main results of Felmer et al. (2012).