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 |
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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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