In this paper, we consider the existence and asymptotic behavior of solutions for the following nonlinear Schrödinger–Poisson system \(\begin{aligned} \left\{ \begin{array}{ll} -\Delta u+V(x)u+\lambda \phi (x)u =\big (a^+(x)+\mu a^-(x)\big )|u|^{p-2}u, \ \ \ & x\in {\mathbb {R}}^3 , \\ -\Delta \phi =u^2, \ & x\in {\mathbb {R}}^3, \end{array} \right. \end{aligned}\) where \(a\in C^{\alpha }({\mathbb {R}}^3,{\mathbb {R}})\ (\alpha \in (0,1))\) is a sign-changing function, \(V\in C({\mathbb {R}}^3,{\mathbb {R}})\) , \(\lambda \) , \(\mu \) are positive parameters and \(p\in (4,6)\) . Using quantitative deformation lemma and degree theory, we prove the existence of a positive ground state solution and a least energy sign-changing solution. Moreover, the asymptotic behavior of the two solutions as \(\lambda \rightarrow 0^+\) or \(\mu \rightarrow +\infty \) are analyzed. In addition, when the set \(\{x\in {\mathbb {R}}^3:\ a(x)>0\}\) possesses several disjoint components, we give the existence and asymptotic behavior of multi-bump sign-changing solutions.
