Ground state solutions of a critical problem involving cylindrical weights

We prove some existence and non-existence results for a nonlinear elliptic equation involving cylindrical weights and critical growth. More precisely, defining ξ=(x,y)∈Rk×RN−kξ=(x,y)∈Rk×RN−k, we study the variational problem {−div(|x|a∇u)=λ|x|a−2u+|x|−bup−1in RN,x≠0u≥0 under suitable assumptions for the parameters p∈(2,2∗]p∈(2,2∗] and a,λ,b∈Ra,λ,b∈R. We firstly consider the strongly elliptic case a=0a=0.