In this paper, we use the minimax method and certain analysis techniques to establish the uniqueness of solutions for a class of (strongly) singular Kirchhoff equations with the Kohn–Laplace operator in the $n$-Heisenberg group and further deduce that the solution is cylindrically symmetric under some necessary structural conditions for a Kohn–Laplace equation with singularity.

In this paper, we studied the existence of solutions for a nonlocal sub-Laplacian system with critical growth and logarithmic perturbation. That is to say, by using the symmetric mountain pass lemma, we proved that under some suitable conditions, the nonlocal sub-Laplacian system admits a sequence $\{z_k\}$ of nontrivial solutions satisfying $\underset{k\to \mathrm{\infty }}{lim}{z}_k=0$. To the best of our knowledge, this result is new even in the Euclidean case.