Asymptotic estimates and nonexistence results for critical problems with Hardy term involving Grushin-type operators

We provide the asymptotic behavior of solutions, at the singularity and at infinity, for a class of subelliptic Dirichlet problems with Hardy perturbation and critical nonlinearity of the type −Lαu−μψ^2/d^2u=K(z)|u|^(2∗−2)u in Ω, where Lα=Δx+|x|2αΔy, α>0 is the so-called Grushin operator, Ω is an open subset of R^N, 0∈Ω, d is the gauge norm naturally associated with Lα, ψ:=|∇αd|, where ∇α is the Grushin gradient, K∈L∞ and 0≤μ< mus$, where mus is the best Hardy constant for Lα. Furthermore, we establish some Pohozaev-type non-existence results.