A note on borderline Brezis-Nirenberg type problems

This note concerns the existence of positive solutions for the boundary problems {−LAu=u2∗−1+λuinΩu=0on∂Ω,{−La,pu=up∗−1+λup−1inΩu=0on∂Ω, where LAu=div(A(x)∇u) and La,pu=div(a(x)|∇u|p−2∇u) are, respectively, linear and quasilinear uniformly elliptic operators in divergence form in a non-smooth bounded open subset Ω of Rn, 1