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

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