Multiple semiclassical solutions for a nonlinear Choquard equation with magnetic field

Article type: Research Article

Authors: Alves, Claudianor O.^a | Figueiredo, Giovany M.^{b; *} | Yang, Minbo^c

Affiliations: [a] Unidade Acadêmica de Matemática, Universidade Federal de Campina Grande, 58109-970, Campina Grande – PB, Brazil. E-mail: coalves@dme.ufcg.edu.br | [b] Faculdade de Matemática, Universidade Federal do Pará, 66075-110, Belém – PA, Brazil. E-mail: giovany@ufpa.br | [c] Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, P.R. China. E-mail: mbyang@zjnu.cn

Correspondence: [*] Corresponding author: Giovany M. Figueiredo, Faculdade de Matemática, Universidade Federal do Pará, 66075-110, Belém – PA, Brazil. E-mail: giovany@ufpa.br.

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

DOI: 10.3233/ASY-151337

Journal: Asymptotic Analysis, vol. 96, no. 2, pp. 135-159, 2016