  This paper is devoted to study a class of integral type Brezis-Nirenbreg
problem on the Heisenberg group. It is a class of new nonlinear integral
equations on the bounded domains of Heisenberg group and related to the CR
Yamabe problems on the CR manifold. Based on the sharp Hardy-Littlewood-Sobolev
inequalities, the nonexistence and existence results are obtained by Pohozaev
type identity, variational method and blow-up analysis, respectively.
