Electron. J. Differential Equations, Vol. 2022 (2022), No. 43, pp. 125.
Existence of solutions for a problem with multiple singular weighted pLaplacians
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 (pq)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 mountainpass theorem;
then, we prove that the PalaisSmale 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;(pq)Laplacian;
variational methods; singular elliptic equation; vanishing potential;
penalization method; Moser iteration scheme.
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Maria José Alves
Colégio Técnico
Universidade Federal de Minas Gerais
Av. Antônio Carlos, 6627, CEP 31270901
Belo Horizonte, MG, Brasil
email: mariajose@ufmg.br


Ronaldo B. Assunção
Departamento de Matemática
Universidade Federal de Minas Gerais
Av. Antônio Carlos, 6627, CEP 31270901
Belo Horizonte, MG, Brasil
email: ronaldo@mat.ufmg.br

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