Alves, Maria JoseAssuncao, Ronaldo B.2023-04-182023-04-182022-06-30Alves, M. J., & Assunção, R. B. (2022). Existence of solutions for a problem with multiple singular weighted p-Laplacians and vanishing potentials. <i>Electronic Journal of Differential Equations, 2022</i>(43), pp. 1-25.1072-6691https://hdl.handle.net/10877/16602This 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.Text25 pages1 file (.pdf)enAttribution 4.0 InternationalQuasilinear elliptic equations with singularities(p-q)-LaplacianVariational methodsSingular elliptic equationVanishing potentialPenalization methodMoser iteration schemeArticle