In this paper, we prove Liouville type theorem of positive weak solution of nonlinear system for Grushin operator. We give some integral inequalities, which combine the method of moving plane with the integral inequality to get the result for nonlinear system.

In this paper, we considered the Neumann boundary value problem for the strongly-coupled subelliptic system and the predator-prey subelliptic system on the Heisenberg group. We provide a priori estimates and the non-existence result for non-constant positive solutions for the strongly-coupled and predator-prey systems.