Liouville theorems to system of elliptic differential inequalities on the Heisenberg group

Abstract

In this paper, we establish Liouville theorems for the following system of elliptic differential inequalities $${\Delta }_{\mathbb{H}}{u}^{m_1}+|\eta {|}_{\mathbb{H}}^{{\gamma }_1}|v{|}^p\le 0,$$ $${\Delta }_{\mathbb{H}}{v}^{m_2}+|\eta {|}_{\mathbb{H}}^{{\gamma }_2}|u{|}^q\le 0,$$ on different unbounded open domains of Heisenberg group $\mathbb{H}$, including the whole space, and half space of $\mathbb{H}$. Here $p>m_2>0$, $q>m_1>0$.