Existence results for the Klein-Gordon-Maxwell equations in higher dimensions with critical exponents

TL;DR

This paper investigates the existence of radially symmetric solitary waves in higher-dimensional space for coupled Klein-Gordon and Maxwell equations with critical nonlinear growth, addressing challenges due to lack of compactness.

Contribution

It establishes existence results for solutions in a challenging critical growth setting, advancing understanding of nonlinear wave equations in higher dimensions.

Findings

Existence of radially symmetric solitary waves proven.

Addresses compactness issues in variational methods.

Results applicable to higher-dimensional nonlinear field theories.

Abstract

In this paper we study the existence of radially symmetric solitary waves in R^N for the nonlinear Klein-Gordon equations coupled with the Maxwell's equations when the nonlinearity exhibits critical growth. The main feature of this kind of problem is the lack of compactness arising in connection with the use of variational methods.