@article{Jiao2024, 
author = {Hongying Jiao and Shuhai Zhu and Jinguo Zhang},
title = {Existence of infinitely many solutions for critical sub-elliptic systems via genus theory},
year = {2024},
journal = {Communications in Analysis and Mechanics},
volume = {16},
number = {2},
pages = {237-261},
keywords = {sub-Laplacian problem, critical exponents, genus theory, carnot groups},
url = {https://www.sciopen.com/article/10.3934/cam.2024011},
doi = {10.3934/cam.2024011},
abstract = {We are devoted to the study of the following sub-Laplacian system with Hardy-type potentials and critical nonlinearities   {−ΔGu−μ1ψ2ud(z)2=λ1ψα|u|2∗(α)−2ud(z)α+βp1f(z)ψγ|u|p1−2u|v|p2d(z)γinG,−ΔGv−μ2ψ2vd(z)2=λ2ψα|v|2∗(α)−2vd(z)α+βp2f(z)ψγ|u|p1|v|p2−2vd(z)γinG,where  −ΔG is the sub-Laplacian on Carnot group  G,  μ1,  μ2∈[0,μG),  α,γ∈(0,2),  λ1,  λ2,  β,  p1,  p2>0 with  1<p1+p2<2,  d(z) is the  ΔG-gauge,  ψ=|∇Gd(z)|,  2∗(α):=2(Q−α)Q−2 is the critical Sobolev-Hardy exponents, and  μG=(Q−22)2 is the best Hardy constant on  G. By combining a variant of the symmetric mountain pass theorem with the genus theory, we prove the existence of infinitely many weak solutions whose energy tends to zero when  β or  λ1,  λ2 belong to a suitable range.}
}