Existence results for theKlein-Gordon-Maxwell equations in higher dimensions with criticalexponents

Paulo Cesar Carrião; Patrícia L. Cunha; Olímpio Hiroshi Miyagaki

doi:10.3934/cpaa.2011.10.709

Article Contents

2011, Volume 10, Issue 2: 709-718. Doi: 10.3934/cpaa.2011.10.709

This issue Previous Article An eigenvalue problem possessing a continuous family of eigenvalues plus an isolated eigenvalue Next Article On existence and nonexistence of the positive solutions of non-newtonian filtration equation

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

1.
Departamento de Matematica, Universidade Federal de Minas Gerais, 31270-010 Belo Horizonte-MG
2.
Departamento Matemática, Universidade Federal de São Carlos, São Carlos, SP 13565-905
3.
Departamento de Matematica, Universidade Federal de Vicosa, 36371-000 Vicosa-MG

Received: April 30, 2010

Revised: July 31, 2010

Published: February 2011

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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.

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Mathematics Subject Classification: Primary: 35J47, 35J50, 35B33; Secondary: 81Q05, 34B18.

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