Ground states for Schrodinger-Poisson systems with three growth terms

Abstract

In this article we study the existence and nonexistence of ground states of the Schrodinger-Poisson system $$\displaylines{ -\Delta u+V(x)u+K(x)\phi u=Q(x)u^3,\quad x\in \mathbb{R}^3,\cr -\Delta\phi=K(x)u^2, \quad x\in \mathbb{R}^3, }$$ where V, K, and Q are asymptotically periodic in the variable x. The proof is based on the the method of Nehari manifold and concentration compactness principle. In particular, we develop the method of Nehari manifold for Schrodinger-Poisson systems with three times growth.

Keywords

• Schrodinger-Poisson system
• variational method
• ground state
• asymptotically periodic