Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 14, pp. 1-14.

Title: Existence of solutions to quasilinear Schrodinger equations with exponential nonlinearity

Authors: Uberlandio B. Severo (Univ. Federal da Paraiba, Brazil)  
         Bruno H. C. Ribeiro  (Univ. Federal da Paraiba, Brazil)
         Diogo de S. Germano  (Univ. Federal de Campina Grande, Brazil)

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 05, 2024.
Math Subject Classifications: 35J20, 35J25, 35J50.
Key Words: Quasilinear Schrodinger equation; fixed point theorem; Trudinger-Moser inequality.