Existence and asymptotic properties of solutions to multiple critical sub-Laplacian systems with Hardy-type potential on stratified Lie groups

Abstract

where - Δ G is a sub-Laplacian on Carnot group G, μ ∈ [ 0 , μ G ) , d is the Δ G -natural gauge, ψ is the weight function defined as ψ : = | ∇ G d | . By analytic technics and variational methods, the extremals of the corresponding best Sobolev constant are found, the existence of positive solution to the system is established. Moreover, by the Moser iteration method, some asymptotic properties of its nontrivial solution at the singular point are verified.