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

In this paper, we study the existence of positive ground state solutions for the nonlinear fractional Schrödinger equation: (-▵)αu+V(x)u=f(u),inRN, where N≥2, α∈(0,1), f∈C1(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.