A multiplicity result for a nonlinear fractional Schrödinger equation in [formula omitted] without the Ambrosetti–Rabinowitz condition.

In this paper we study the existence and the multiplicity of positive solutions for the following class of fractional Schrödinger equations ϵ 2 s ( − Δ ) s u + V ( x ) u = f ( u ) in R N , where ϵ > 0 is a parameter, s ∈ ( 0 , 1 ) , N > 2 s , V : R N → R is a continuous positive potential, and f : R → R is a C 1 superlinear nonlinearity which does not satisfy the Ambrosetti–Rabinowitz condition. The main result is established by using minimax methods and Ljusternik–Schnirelmann theory of critical points. [ABSTRACT FROM AUTHOR]