In this paper, we consider the following nonlinear fractional p-Laplacian equation of Schrödinger-type
\begin{equation*} (-\Delta)_p^s u + V(x)|u|^{p-2}u =k(x){|u|}^ {\eta-2}u+ f(x,u), \ \ \qquad \ x \in \mathbb{R}^N \\ \end{equation*}
where 0 < s < 1 < η < p, N ≥ 2, V (x) is a real continuous function on $\mathbb{R}^N$. Based on some assumptions on n k, V and f we obtain the existence of non-trivial solutions using of the variational methods.
2010 Mathematics Subject Classifications: 35J05; 35J10; 35A15.