@article{Shi2025, 
author = {Wei Shi},
title = {Nonexistence results of nonnegative solutions of elliptic equations and systems on the Heisenberg group},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {5},
pages = {12576-12597},
keywords = {quasilinear elliptic inequalities, elliptic systems, Heisenberg group},
url = {https://www.sciopen.com/article/10.3934/math.2025567},
doi = {10.3934/math.2025567},
abstract = {This paper establishes sharp nonexistence criteria for nonnegative solutions to a class of quasilinear elliptic inequalities and divergence-type systems in the subelliptic framework of the Heisenberg group        H    n  . By developing an optimized test function methodology adapted to the stratified Lie group structure, nonexistence is established through a contradiction argument based on maximum principle-type inequalities. The analysis contributes new insights into the role of sub-Riemannian geometry in constraining the solution behavior for degenerate elliptic operators.}
}