Positive Ground State Solutions for a Schrödinger-Newton System with Negative Critical Nonlocal Term

Abstract

We consider the following Schrödinger-Newton system with negative critical nonlocal term

$\left\{\begin{array}{ll}-\Delta u-\phi|u|^{3} u=a(x) f(u), & \text { in } \mathbb{R}^{3} \\-\Delta \phi=|u|^{5}, & \text { in } \mathbb{R}^{3}\end{array}\right.$

where a and f satisfy some certain conditions. By using the variational method and analytical techniques, we obtain the existence of positive ground state solutions which improves the recent results in the literature.

Keywords

Schrödinger-Newton system / critical nonlocal term / variational method / ground state solution