Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 43, pp. 1-25.

Title: Existence of solutions for a problem with multiple singular weighted p-Laplacians
       and vanishing potentials
       
Authors: Maria Jose Alves    (Univ. Federal de Minas Gerais, Belo Horizonte, MG, Brasil)
         Ronaldo B. Assuncao (Univ. Federal de Minas Gerais, Belo Horizonte, MG, Brasil)

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.