Multiple positive solutions for a quasilinear elliptic problem involving critical Sobolev–Hardy exponents and concave–convex nonlinearities

Let Ω⊂RNΩ⊂RN (N≥3N≥3) be a bounded smooth domain containing the origin. In this paper, by using variational methods, the multiplicity of positive solutions is obtained for a quasilinear elliptic problem −Δpu−μ|u|p−2u|x|p=|u|p∗(t)−2|x|tu+λ|u|q−2|x|su,u∈W01.p(Ω), with Dirichlet boundary condition, where Δpu=div(|∇u|p−2∇u), 10λ>0, 0≤s,t