In this paper, we consider the following Kirchhoff–Schrödinger–Poisson system: \(\begin{aligned} \left\{ \begin{array}{ll} \displaystyle -\left( a+b\int _{\mathbb {R}^{3}}|\nabla u|^{2}\textrm{d}x\right) \Delta u+ u+\mu K(x) \phi u=f(x)|u|^{p-2}u+g(x)|u|^{q-2}u & \text { in }\mathbb {R}^{3},\\ -\Delta \phi =K(x)u^{2} & \text { in }\mathbb {R}^{3},\\ \end{array} \right. \end{aligned}\) where \(a,b,\mu >0\) , \(1<q<2<p<\min \{4, 2^{*}\}\) , \(2^{*}=2N/(N-2)\) . Under some suitable conditions on functions K, f, and g, we first prove that a bounded Palais–Smale sequence possesses a convergent subsequence by a novel method. Then two negative-energy nontrivial solutions are obtained via the Ekeland variational principle. Furthermore, by imposing some additional assumptions on g and combining the filtration of Nehari manifold, we can prove that the corresponding energy functional is bounded below on a sub-manifold of Nehari manifold and get three nontrivial solutions for the above problem.
