Multiple solutions of nonlinear Schrödinger equation with the fractional Laplacian

In this paper we are devoted to a time-independent fractional Schrödinger equation (−Δ)αu+V(x)u=f(x,u)in  RN, where (−Δ)α(−Δ)α stands for the fractional Laplacian of order α∈(0,1)α∈(0,1), ff is either asymptotically linear or superquadratic growth. Under appropriate assumptions on VV and ff, we prove the existence of infinitely many nontrivial high or small energy solutions, which extend and complement previously known results in the literature.