@article{Zhu2024, 
author = {Shuhai Zhu},
title = {Doubly critical problems involving Sub-Laplace operator on Carnot group},
year = {2024},
journal = {Electronic Research Archive},
volume = {32},
number = {8},
pages = {4969-4990},
keywords = {doubly critical problem, carnot group, hardy potential, pohozaev identity, variational method},
url = {https://www.sciopen.com/article/10.3934/era.2024229},
doi = {10.3934/era.2024229},
abstract = {This paper was focused on the solvability of a class of doubly critical sub-Laplacian problems on the Carnot group  G:   −ΔGu−μψ2(ξ)ud(ξ)2=|u|p−2u+ψα(ξ)|u|2∗(α)−2ud(ξ)α,u∈S1,2(G).Here,  p∈(1,2∗],  α∈(0,2),  μ∈[0,μG),  2∗=2QQ−2, and  2∗(α)=2(Q−α)Q−2. By means of variational techniques, we extended the arguments developed in [1]. In addition, we also established the existence result for the subelliptic system which involved sub-Laplacian and critical homogeneous terms.}
}