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Schrödinger-Poisson systems in dimension d ≦ 3: The whole-space case

Published online by Cambridge University Press:  14 November 2011

F. Nier
F. Nier
Affiliation:
CMAP-Ecole Poly technique, URA-CNRS 756, F-91128 Palaiseau Cedex, France
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Synopsis

After a study made for bounded domains and in the periodic case, we investigate the variational formulation of Schrödinger-Poisson systems set on the whole space ℝd, d ≦ 3. This variational formulation leads to a uniqueness result, while the existence of a solution is proved only for ‘small data’ because of the lack of coerciveness. The end of this paper briefly presents the extension of this formalism to a physically relevant problem where the potential is periodic in one direction.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 6 , 1993 , pp. 1179 - 1201
Copyright
Copyright © Royal Society of Edinburgh 1993

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