Electron. J. Differential Equations, Vol. 2024 (2024), No. 14, pp. 1-14.

Existence of solutions to quasilinear Schrodinger equations with exponential nonlinearity

Uberlandio B. Severo, Bruno H. C. Ribeiro, Diogo de S. Germano

Abstract:
In this article we study the existence of solutions to quasilinear Schrodinger equations in the plane, involving a potential that can change sign and a nonlinear term that may be discontinuous and exhibit exponential critical growth. To prove our existence result, we combine the Trudinger-Moser inequality with a fixed point theorem.

Submitted March 7, 2023. Published February 5, 2024.
Math Subject Classifications: 35J20, 35J25, 35J50.
Key Words: Quasilinear Schrodinger equation; fixed point theorem; Trudinger-Moser inequality.
DOI: 10.58997/ejde.2024.14

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Uberlandio B. Severo
Universidade Federal da Paraíba
Departamento de Matemática
CEP 58051-900, João Pessoa - PB, Brazil
email: uberlandio@mat.ufpb.br
Bruno H. C. Ribeiro
Universidade Federal da Paraíba
Departamento de Matemática
CEP 58051-900, João Pessoa - PB, Brazil
email: bruno@mat.ufpb.br
Diogo de S. Germano
Universidade Federal de Campina Grande
Unidade Académica de Matemática
CEP 58109-970, Campina Grande - PB, Brazil
email: diogosg@mat.ufcg.edu.br

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