English

Liouville type theorems for subelliptic systems on the Heisenberg group with general nonlinearity

Analysis of PDEs 2023-03-09 v1

Abstract

In this paper, we establish Liouville type results for semilinear subelliptic systems associated with the sub-Laplacian on the Heisenberg group Hn\mathbb{H}^{n} involving two different kinds of general nonlinearities. The main technique of the proof is the method of moving planes combined with some integral inequalities replacing the role of maximum principles. As a special case, we obtain the Liouville theorem for the Lane-Emden system on the Heisenberg group Hn\mathbb{H}^{n}, which also appears to be a new result in the literature.

Keywords

Cite

@article{arxiv.2303.04210,
  title  = {Liouville type theorems for subelliptic systems on the Heisenberg group with general nonlinearity},
  author = {Rong Zhang and Vishvesh Kumar and Michael Ruzhansky},
  journal= {arXiv preprint arXiv:2303.04210},
  year   = {2023}
}