Critical growth problems with singular nonlinearities on Carnot groups

We provide regularity, existence and non existence results for the semilinear subelliptic problem with critical growth −ΔGu=ψ^α|u|^(2∗(α)−2)u/d(ξ)^α+λu in ΩΩ, u=0 on ∂Ω, where ΔG is a sublaplacian on a Carnot group GG, 0<2, 2∗(α)=2(Q−α)/(Q−2), Ω is a bounded domain of G, d is the natural gauge associated with the fundamental solution of −ΔG on G and ψ:=|∇Gd|, ∇G being the subelliptic gradient associated to ΔG, λ is a real parameter.