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Improved estimates and a limit case for the electrostatic Klein–Gordon–Maxwell system

Published online by Cambridge University Press:  03 June 2011

A. Azzollini ,
L. Pisani  and
A. Pomponio
A. Azzollini
Affiliation:
Dipartimento di Matematica ed Informatica, Università degli Studi della Basilicata, Via dell'Ateneo Lucano 10, 85100 Potenza, Italy ([email protected])
L. Pisani
Affiliation:
Dipartimento di Matematica, Università degli Studi di Bari, Via E. Orabona 4, 70125 Bari, Italy ([email protected])
A. Pomponio
Affiliation:
Dipartimento di Matematica, Politecnico di Bari, Via E. Orabona 4, 70125 Bari, Italy ([email protected])
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Abstract

We study the class of nonlinear Klein–Gordon–Maxwell systems describing a standing wave (charged matter field) in equilibrium with a purely electrostatic field. We improve some previous existence results in the case of an homogeneous nonlinearity. Moreover, we deal with a limit case, namely when the frequency of the standing wave is equal to the mass of the charged field; this case shows analogous features of the well-known ‘zero-mass case’ for scalar field equations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 3 , June 2011 , pp. 449 - 463
Copyright
Copyright © Royal Society of Edinburgh 2011

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