A multiplicity result for a nonlinear fractional Schrödinger equation in RN 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 equationsϵ2s(−Δ)su+V(x)u=f(u) in RN, where ϵ>0 is a parameter, s∈(0,1), N>2s, V:RN→R is a continuous positive potential, and f:R→R is a C1 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.