Multiple solutions for singularly perturbed nonlinear magnetic Schrödinger equations

Article type: Research Article

Authors: Ambrosio, Vincenzo^{; *}

Affiliations: Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche, 12, 60131 Ancona, Italy. E-mail: v.ambrosio@univpm.it

Correspondence: [*] Corresponding author. E-mail: v.ambrosio@univpm.it.

Abstract: In this paper we consider singularly perturbed nonlinear Schrödinger equations with electromagnetic potentials and involving continuous nonlinearities with subcritical, critical or supercritical growth. By means of suitable variational techniques, truncation arguments and Lusternik–Schnirelman theory, we relate the number of nontrivial complex-valued solutions with the topology of the set where the electric potential attains its minimum value.

Keywords: Magnetic Laplacian, Variational methods, Lusternik–Schnirelman theory

DOI: 10.3233/ASY-211705

Journal: Asymptotic Analysis, vol. 128, no. 2, pp. 239-272, 2022