Multiple solutions of nonlinear Schrödinger equation with the fractional Laplacian. (August 2016) - Ge, Bin
Abstract: In this paper we are devoted to a time-independent fractional Schrödinger equation ( − Δ ) α u + V ( x ) u = f ( x, u ) in  R N, where ( − Δ ) α stands for the fractional Laplacian of order α ∈ ( 0, 1 ), f is either asymptotically linear or superquadratic growth. Under appropriate assumptions on V and f, we prove the existence of infinitely many nontrivial high or small energy solutions, which extend and complement previously known results in the literature.