This paper investigates the existence of solutions to the Schrödinger–Poisson system on the Heisenberg group: \(\begin{aligned} \left\{ \begin{array}{ll} -\Delta _{H,p} u+ V(\xi )|u|^{p-2}u + \mu \phi |u|^{p-2} u = K(\xi )|u|^{r-2}u + f(\xi ,u), & \xi \in \mathbb {H}^n,\\ -\Delta _H \phi = u^p, & \xi \in \mathbb {H}^n, \end{array} \right. \end{aligned}\) where \(\Delta _{H,p}u =\text {div}_H(|D_H u|^{p-2}_{H}D_H u)\) denotes the \(p\) -sub-Laplacian, \(1< r< p < Q\) , \(\mu \) is a real parameter and \(Q = 2n + 2\) is the homogeneous dimension of \(\mathbb {H}^{n}\) . Under appropriate assumptions about the functions \(V\) , \(K\) and \(f\) , and by employing the Ekeland variational principle together with the mountain pass theorem in the framework of classical Sobolev spaces on the Heisenberg group, we establish the existence of nontrivial solutions for this system. To some extent, our results extend previous work of Sun et al. (J Math Anal Appl 442:385–403, 2016) and Solukia et al. (J Elliptic Parabolic Equ 10:211–224, 2024).
