This paper is concerned with the following nonlocal
Schr\”{o}dinger-Poisson type system:
\begin{equation*} \begin{cases}
-\left(a-b\int_{\Omega}|\nabla_{H}u|^{2}dx\right)\Delta_{H}u+\mu\phi
u=\lambda|u|^{q-2}u,
&\mbox{in} \
\Omega,\\
-\Delta_{H}\phi=u^2 &
\mbox{in}\
\Omega,\\
u=\phi=0 & \mbox{on}\
\partial\Omega,
\end{cases} \end{equation*} where $a,
b>0$ and $\Delta_H$ is the
Kohn-Laplacian on the first Heisenberg group
$\mathbb{H}^1$,
$\Omega\subset
\mathbb{H}^1$ is a smooth bounded domain,
$\lambda>0$,
$\mu\in \mathbb{R}$ are
some real parameters and $1“”
Marcinkiewicz multipliers associated with the Kohn Laplacian on the Shilov boundary of the product domain in $$\mathbb {C}^{2n}$$
