Electron. J. Differential Equations, Vol. 2022 (2022), No. 43, pp. 1-25.

Existence of solutions for a problem with multiple singular weighted p-Laplacians and vanishing potentials

Maria Jose Alves, Ronaldo B. Assuncao

Abstract:
This work establishes the existence of positive solutions to a quasilinear singular elliptic equations involving the (p-q)-Laplacian operator with singularities and a vanishing potential. We adapt the penalization method developed by del Pino and Felmer and we consider an auxiliary problem whose corresponding functional satisfies the geometry of the mountain-pass theorem; then, we prove that the Palais-Smale sequences are bounded in a Sobolev space; after that, we show that the auxiliary problem has a solution. Finally, we use the Moser iteration scheme to obtain an appropriate estimate and we conclude that the solution to the auxiliary problem is also a solution to the original problem.

Submitted August 16, 2021. Published June 30, 2022.
Math Subject Classifications: 35J20, 35J75, 35J92, 35J10, 35B09, 35B38, 35B45.
Key Words: Quasilinear elliptic equations with singularities;(p-q)-Laplacian; variational methods; singular elliptic equation; vanishing potential; penalization method; Moser iteration scheme.
DOI: https://doi.org/10.58997/ejde.2022.43

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Maria José Alves
Colégio Técnico
Universidade Federal de Minas Gerais
Av. Antônio Carlos, 6627, CEP 31270-901
Belo Horizonte, MG, Brasil
email: mariajose@ufmg.br
Ronaldo B. Assunção
Departamento de Matemática
Universidade Federal de Minas Gerais
Av. Antônio Carlos, 6627, CEP 31270-901
Belo Horizonte, MG, Brasil
email: ronaldo@mat.ufmg.br

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