Schrödinger-Poisson systems in dimension d ≦ 3: The whole-space case
Francis Nier · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1993
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.