Existence of positive ground state solutions for fractional Schrödinger equations with a general nonlinearity. Issue 7 (19th May 2018) - Liu, Zhisu; Ouyang, Zigen
ABSTRACT: In this paper, we study the existence of positive ground state solutions for the nonlinear fractional Schrödinger equation: ( - ▵ ) α u + V ( x ) u = f ( u ), in R N, where N ≥ 2, α ∈ ( 0, 1 ), f ∈ 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.