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Abstract

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.

Keywords

Choquard equation magnetic field variational methods penalization techniques Ljusternik–Schnirelmann theory

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Multiple semiclassical solutions for a nonlinear Choquard equation with magnetic field

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