Solutions for a nonhomogeneous nonlinear Schroedinger equation with double power nonlinearity

Abstract

We consider the problem $- \Delta u+V(x)u=f^{\prime}(u)+g(x)$ in $\mathbb R^N$, under the assumption $\lim_{x\rightarrow\infty}V(x)=0$, and with the nonlinear term $f$ with a double power behavior. We prove the existence two solutions when $g$ is sufficiently small and $V < 0$.