Positive ground state solutions for the critical Klein-Gordon-Maxwell system with potentials

TL;DR

This paper establishes the existence of positive ground state solutions for a critical Klein-Gordon-Maxwell system with periodic potentials, using variational methods and critical point theory.

Contribution

It introduces a novel approach combining Nehari manifold minimization with Brézis-Nirenberg techniques for this class of nonlinear systems.

Findings

Existence of positive ground state solutions proven

Method applicable to systems with critical growth nonlinearities

Results extend understanding of Klein-Gordon-Maxwell systems with potentials

Abstract

This paper deals with the Klein-Gordon-Maxwell system when the nonlinearity exhibits critical growth. We prove the existence of positive ground state solutions for this system when a periodic potential V is introduced. The method combines the minimization of the corresponding Euler-Lagrange functional on the Nehari manifold with the Br\'ezis and Nirenberg technique