Multiple positive solutions for a quasilinear nonhomogeneous Neumann problems with critical Hardy exponents

In this paper, we study the existence, nonexistence and multiplicity of positive solutions for nonhomogeneous Neumann boundary value problems of the type {−Δpu+λup−1=uq|x|sx∈Ω,u>0x∈Ω,|∇u|p−2Dγu=ϕx∈∂Ω∖{0}, where Ω is a bounded domain in Rn with smooth boundary, 0∈∂Ω, 2≤p