Ground states for a class of asymptotically periodic Schrödinger–Poisson systems with critical growth

Abstract

The purpose of this paper is to study the existence of ground state solution for the Schr\"{o}dinger–Poisson systems: \[\begin{cases} -\Delta u+V(x)u+K(x)\phi u=Q(x)|u|^{4}u+f(x,u),&x\in\mathbb{R}^{3},\\ -\Delta\phi=K(x)u^{2},&x\in\mathbb{R}^{3}, \end{cases} \] where $V(x)$, $K(x)$, $Q(x)$ and $f(x,u)$ are asymptotically periodic functions in $x$.

Keywords

• schrödinger–poisson systems
• ground state solution
• variational methods