Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 23, Issue 10, Pages 1915-1938Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202513500541
Keywords
Steady states; variational methods; subadditivity inequality; constrained minimization; sharp nonexistence. L-2-norm constraint; Schrodinger-Poisson; Maxwell-Schrodinger; Schrodinger-Poisson-X-alpha; concentration-compactness; standing waves; semiconductors; plasma physics
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Funding
- MINECO (Spain) [MTM2011-23384]
- ANR project NoNAP (France)
- ANR project STAB (France)
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This paper reviews recent results and open problems concerning the existence of steady states to the Maxwell-Schrodinger system. A combination of tools, proofs and results are presented in the framework of the concentration-compactness method.
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