Local Behavior of Solutions to Subelliptic Problems with Hardy Potential on Carnot Groups

We determine the exact behavior at the singularity of solutions to semilinear subelliptic problems of the type -ΔGu-μψ2/d2u=f(ξ,u) in Ω , u= 0 on ∂Ω , where ΔG is a sub-Laplacian on a Carnot group G of homogeneous dimension Q, Ω is an open subset of G, 0 ∈ Ω , d is the gauge norm on G, ψ: = |∇Gd| , where ∇Gis the horizontal gradient associated with ΔG, f has at most critical growth and 0 ≤ μ< μ¯ , where μ¯=(Q-2/2)^2 is the best Hardy constant on G.