  The goal of this paper is to establish singular Adams type inequality for
biharmonic operator on Heisenberg group. As an application, we establish the
existence of a solution to \begin{equation*} \Delta_{\mathbb{H}^n}^2
u=\frac{f(\xi,u)}{\rho(\xi)^a}\,\,\text{ in }\Omega,\,\,
u|_{\partial\Omega}=0=\left.\frac{\partial u}{\partial
\nu}\right|_{\partial\Omega}, \end{equation*} where $0\in \Omega \subseteq
\mathbb{H}^4$ is a smooth bounded domain, $0\leq a<Q,\,(Q=10).$ The special
feature of this problem is that it contains an exponential nonlinearity and
singular potential.

Analysis of PDEs