descriptionPublicationkeyboard_double_arrow_right Article , Preprint 12 Jul 2013Embargo end date: 01 Jan 2013 English Publisher:World Scientific Pub Co Pte LtdJournal:Mathematical Models and Methods in Applied Sciences, volume 23, pages 1,915-1,938 (issn: 0218-2025, eissn: 1793-6314,

Authors: Catto, Isabelle; Dolbeault, Jean; Sanchez, Oscar; Soler, Juan;

doi: 10.1142/s0218202513500541 , 10.48550/arxiv.1306.3699

arXiv: http://arxiv.org/abs/1306.3699

EXISTENCE OF STEADY STATES FOR THE MAXWELL–SCHRÖDINGER–POISSON SYSTEM: EXPLORING THE APPLICABILITY OF THE CONCENTRATION–COMPACTNESS PRINCIPLE

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Abstract

This paper reviews 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.

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Keywords

Steady states, 330, variational methods, Standing waves, Schrödinger-Poisson, Analyse, Plasma physics, Sharp nonexistence. L2-norm constraint, constrained minimization, Maxwell-Schrödinger, Mathematics - Analysis of PDEs, Semiconductors, 515, Schrödinger-Poisson-X alpha, subadditivity inequality, FOS: Mathematics, Concentration-Compactness, Analysis of PDEs (math.AP)

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