Non-homogeneous fractional Schr\"odinger equation

Abstract

In this article we are interested on the non-homogeneous fractional Schr\"odinger equation \begin{eqnarray}\label{eq00} &(-\Delta)^{\alpha}u(x) + V(x)u(x) = f(u) + h(x) \mbox{ in } \mathbb{R}^{n}. \end{eqnarray} By using mountain pass Thoerem and Ekeland's variational principle, we prove the existence of two nontrivial solutions for (\ref{eq00}).