Multiple positive solutions for a quasilinear elliptic problem involving critical SobolevHardy exponents and concaveconvex nonlinearities

Let Ω⊂^RN (N<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), 1<p<N, 0≤μ<μ=(^N-pp)p, λ>0, 0≤s,t<p, 1≤q<p and ^p*(t)=p(N-t)N-p is the critical SobolevHardy exponent.