Solutions for nonhomogeneous Kohn-Spencer Laplacian on Heisenberg group

In this paper, we study the existence of at least one bounded weak solution for Kohn-Spencer Laplacian with a weight depending on the solution and convection term of the form\[ -div_{\mathbb{H}<^>n}(\nu(\xi,u) |D_{\mathbb{H}<^>n}u|<^>{p-2}_{\mathbb{H}<^>n}D_{\mathbb{H}<^>n}u)=f(\xi,u,D_{\mathbb{H}<^>n} u) \]-divHn(nu(xi,u)|DHnu|Hnp-2DHnu)=f(xi,u,DHnu)in a bounded domain $ \Omega \subset \mathbb {H}<^>n $ omega subset of Hn. We show the set of solutions is uniformly bounded by a special Moser's iteration.