Existence of positive ground state solutions for fractional Schrodinger equations with a general nonlinearity

In this paper, we study the existence of positive ground state solutions for the nonlinear fractional Schrodinger equation: (-Delta)(alpha)u + V(x)u = f(u), in R-N, where N >= 2, alpha is an element of (0, 1), f is an element of C-1(R, R) is subcritical near infinity and superlinear near zero and satisfies the Berestycki-Lions condition. Using the monotonic trick established by Struwe-Jeanjean, the method of Pohozaev manifold and establishing a global compactness lemma, we show that the above problem has at least a positive ground state solution.