GROUND STATES FOR SUPERLINEAR FRACTIONAL SCHRODINGER EQUATIONS IN RN

In this paper we study ground states of the following fractional Schrodinger equation {(-Delta)(s)u + V(x)u = f(x, u) in R-N, u is an element of H-s(R-N), where s is an element of (0,1), N > 2s and f is a continuous function satisfying a suitable growth assumption weaker than the Ambrosetti-Rabinowitz condition. We consider the cases when the potential V(x) is 1-periodic or has a bounded potential well.