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Multiple semiclassical solutions for a nonlinear Choquard equation with magnetic field. (English) Zbl 1339.35278

Summary: In the present paper, we study the existence of multiple solutions for a nonlinear Choquard equation in the presence of a magnetic field. Using variational methods, penalization techniques and Ljusternik-Schnirelmann theory, we relate the number of solutions with the topology of the set where the potential attains its minimum value.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35A15 Variational methods applied to PDEs
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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