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

Abstract

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).