Existence and non-existence of solitary waves for the critical Klein-Gordon equation coupled with of Maxwell's equations

被引：92

作者：

Cassani, D ^{[1
]}

机构：

[1] Univ Milan, Dip Matemat F Enriques, I-20133 Milan, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2004年 / 58卷 / 7-8期

关键词：

variational methods; nonlinear elliptic systems; Klein-Gordon equation; critical growth; Pohozaev identity; solitary waves;

D O I：

10.1016/j.na.2003.05.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we investigate existence and non-existence of solutions for a nonlinear elliptic system, arising from the coupling of the nonlinear Klein-Gordon equation with the Maxwell equations, when the nonlinearity exhibits critical growth. We prove a non-existence result by a Pohozaev-type argument and then, adding a suitable perturbation, we recover existence of at least a radially symmetric solution. We overcome the lack of compactness relying on the Brezis -Nirenberg method. (C) 2004 Elsevier Ltd. All rights reserved.

引用

页码：733 / 747

页数：15

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