Existence of positive ground state solutions for a class of asymptotically periodic Schrodinger-Poisson systems

Abstract

In this article, by using variational method, we study the existence of a positive ground state solution for the Schr\"odinger-Poisson system $$\displaylines{ -\Delta u+V(x)u+K(x)\phi u=f(x,u),\quad x\in\mathbb{R}^3,\cr -\Delta\phi=K(x)u^2,\quad x\in\mathbb{R}^3, }$$ where V(x), K(x) and f(x,u) are asymptotically periodic functions in x at infinity.

Keywords

• Schrodinger-Poisson systems
• ground state solution
• variational methods