On Positive Solutions For A Singular Quasilinear Elliptic Equation With Critical Sobolev Exponent

In this paper, we deal with the following singular quasilinear elliptic equation: where f2is a bounded domain with smooth bounded in RN, Δpu=div(|▽u|p-2▽u))is p-Laplacian,2≤p<N, λ>0is a real parameter, h(x)=distα(x,(?)Ω)∈L∞(Ω), α-r>0, p*=(?) is the critical Sobolev exponent.Since the corresponding functional of ((?)λ) fails to be Frechet differentiable, the singular problem ((?)λ) becomes more complicated to deal with by the classical critical point theory and we have to overcome more difficulties in the study of positive solutions for ((?)λ), by using the Ekeland variational principle and the technique of the Nehari set decomposition, we overcome the above difficulties and obtain the existence and multiplicity results of positive solutions of...