期刊
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
卷 69, 期 3, 页码 -出版社
SPRINGER BASEL AG
DOI: 10.1007/s00033-018-0975-0
关键词
Schrodinger-Newton equation; Hartree equation; Logarithmic potential; Variational methods; Relaxation
资金
- Projet de Recherche (Fonds de la Recherche Scientifique-FNRS) [T.1110.14]
We consider a nonlinear Choquard equation when the self-interaction potential V is unbounded from below. Under some assumptions on and on , covering and being the one- or two-dimensional Newton kernel, we prove the existence of a nontrivial groundstate solution by solving a relaxed problem by a constrained minimization and then proving the convergence of the relaxed solutions to a groundstate of the original equation.
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