Anderson de Araujo1, Luiz Faria2, Aldo Medeiros3, Dumitru Motreanu4
The article is dedicated to the memory of Professor Haim Brezis
Abstract. The paper provides the existence of a positive weak solution and a priori estimates for a class of parametric Dirichlet problems with unbounded variable exponents and exhibiting exponential growth. The approach relies on a special sub-supersolution method that we develop in our general setting. The bound of the admissible values of the parameter is explicitly determined. Applications to the regularity properties and asymptotic behavior with respect to the parameter are also given. Examples demonstrate the applicability of the stated results.
Keywords: Dirichlet problem, positive solution, sub-supersolution, exponential growth, supercritical growth, unbounded variable exponent.
MSC: 35J62, 35B51, 35B33.
DOI 10.56082/annalsarscimath.2025.1.279
1 anderson.araujo@ufv.br, Departamento de Matematica, UFV, CCE, 36570-900, Vicosa, MG, Brazil
2 luiz.faria@ufjf.br, Departamento de Matematica, UFJF, ICE, 36036-330, Juiz de Fora, MG, Brazil
3 aldo.medeiros@ufv.br, Departamento de Matematica, UFV, CCE, 36570-900, Vicosa, MG, Brazil
4 motreanu@univ-perp.fr, Departement de Mathematiques, Universite de Perpignan, Via Domitia, Perpignan, 66860, France
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 17 no 1, 2025
