Published in
World Scientific Publishing, Mathematical Models and Methods in Applied Sciences, 10(23), p. 1915-1938, 2013
DOI: 10.1142/s0218202513500541
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Existence of steady states for the Maxwell-Schr̈odinger-Poisson system: exploring the applicability of the concentration-compactness principle
Journal article published in 2013 by
Isabelle Catto,
Óscar Sánchez,
Jean Dolbeault 
,
O. Sánchez,
Óscar Sánchez,
Juan Soler
,
O. Sánchez,
Óscar Sánchez,
Juan Soler
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Abstract
This paper is intended to review recent results and open problems concerning the existence of steady states to the Maxwell-Schrödinger system. A combination of tools, proofs and results are presented in the framework of the concentration--compactness method.