Nonlinear Schrödinger equations involving exponential critical growth with unbounded or vanishing potentials

Article type: Research Article

Authors: Anderson Cardoso, J.^a | Carvalho, Jonison Lucas^b | Medeiros, Everaldo^{b; *}

Affiliations: [a] Departamento de Matemática, Universidade Federal de Sergipe, 49000-100, São Cristóvão-SE, Brazil. E-mail: anderson@mat.ufs.br | [b] Departamento de Matemática, Universidade Federal da Paraíba, 58051-900, João Pessoa–PB, Brazil. E-mails: jonison.mat@gmail.com, everaldo@mat.ufpb.br

Correspondence: [*] Corresponding author. E-mail: everaldo@mat.ufpb.br.

Abstract: In this paper we deal with the following class of nonlinear Schrödinger equations −Δu+V(|x|)u=λQ(|x|)f(u),x∈R2, where λ>0 is a real parameter, the potential V and the weight Q are radial, which can be singular at the origin, unbounded or decaying at infinity and the nonlinearity f(s) behaves like eαs2 at infinity. By performing a variational approach based on a weighted Trudinger–Moser type inequality proved here, we obtain some existence and multiplicity results.

Keywords: Nonlinear Schrödinger equation, unbounded or decaying radial potentials, exponential critical growth, weighted Trudinger–Moser type inequality

DOI: 10.3233/ASY-211752

Journal: Asymptotic Analysis, vol. 130, no. 3-4, pp. 297-322, 2022