In this paper we investigate the 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 nonexistence result by a Pohozaev type argument and then, adding a suitable perturbation, we recover the existence of at least a radially symmetric solution. We overcome the lack of compactness relying on the Brezis-Nirenberg method.
Existence and non-existence of solitary waves for the critical Klein-Gordon equation coupled with Maxwell's equations / Daniele Cassani. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 58:7-8(2004), pp. 733-747.
Existence and non-existence of solitary waves for the critical Klein-Gordon equation coupled with Maxwell's equations
Daniele Cassani
2004
Abstract
In this paper we investigate the 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 nonexistence result by a Pohozaev type argument and then, adding a suitable perturbation, we recover the existence of at least a radially symmetric solution. We overcome the lack of compactness relying on the Brezis-Nirenberg method.Pubblicazioni consigliate
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