Positive solutions to the weighted critical quasilinear problems

摘要

In a bounded domain with smooth boundary, we consider a kind of weighted quasilinear elliptic problem, which satisfies Dirichlet boundary condition and involves the Hardy–Sobolev inequality. By the analytic techniques, we first get the properties of the extremal functions by which the best Hardy–Sobolev constant is achieved. Then by the variational methods, the existence of positive solutions to the problem is verified by careful estimates and computations.