Multiple Positive Solutions for Quasilinear Elliptic Problems Involving Concave-Convex Nonlinearities and Multiple Hardy-Type Terms

In this paper, we deal with the existence and multiplicity of positive solutions for the quasilinear elliptic problem-δpu-∑i=1kμi|u|p-2|x-ai|Pu=|u|p*-2u+λ|u|q-2u,x∈Ω, where Ω⊂ℝ^N (N ≥ 3) is a smooth bounded domain such that the different points a_i ∈ Ω, i = 1,2,. .,k, 0 ≤ μ_i < μ-=(N-pp)p,λ>0,1≤q<p,andp*=pNN-p. The results depend crucially on the parameters λ, q and μi for i = 1,2,. .,k.