In this paper, we deal with the planar Schrödinger–Poisson system \(\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u + V(x) u + \phi u = b|u|^{p-2} u \ & \text {in}\ \mathbb {R}^{2},\\ \Delta \phi = u^{2} & \text {in}\ \mathbb {R}^{2}, \end{array}\right. } \end{aligned}\) where \(b \ge 0\) , \(p > 2 \) and \(V \in C(\mathbb {R}^2, \mathbb {R})\) is a potential function with \(\inf _{\mathbb {R}^2} V >0\) . Suppose moreover that V exhibits a bounded potential well in the sense that \(\lim _{|x|\rightarrow \infty } V(x)\) exists and is equal to \(\sup _{\mathbb {R}^2} V\) . By using the variational methods, we obtain the existence of ground state solutions for this system in the case where \(p \ge 3\) . Furthermore, we also present a minimax characterization of ground state solutions. The main feature of this work is that we do not assume any periodicity or symmetry condition on the external potential V, which is essential to establish the compactness condition of Cerami sequences.
