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

[摘要] 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 auxiliaryproblem is also a solution to the original problem.

[学科分类] 数学（综合）

[关键词] Quasilinear elliptic equations with singularities;(p-q)-Laplacian;variational methods;singular elliptic equation;vanishing potential;penalization method;Moser iteration scheme.