Existence of weak solutions to a class of schrodinger type equations involving the fractional p-laplacian in Rⁿ

We are concerned with the following elliptic equations: (-δ)^s _pu + V (x)|u|p^-2u = λg(x; u) in R^N; where (-δ)^s _p is the fractional p-Laplacian operator with 0 < s < 1 < p < +∞, sp < N, the potential function V: R^N → (0, ∞) is a continuous potential function, and g: R^NxR → R satisfies a Caratheodory condition. We show the existence of at least one weak solution for the problem above without the Ambrosetti and Rabinowitz condition. Moreover, we give a positive interval of the parameter λ for which the problem admits at least one nontrivial weak solution when the nonlinearity g has the subcritical growth condition.