In this paper, we focus our attention on following Schrödinger–Poisson system: $\left\{\begin{array}{c}-{\epsilon }^2\Delta u+V\left(x\right)u+\lambda \psi u={\left|u\right|}^{p-2}u,x\in {\mathbb{R}}^3,\hfill \\ -{\epsilon }^2\Delta \psi =u^2,u\in H^1\left({\mathbb{R}}^3\right).\hfill \end{array}\right.$where $4<p<6$ and $\epsilon ,\lambda >0$ are small positive parameters. Under a local condition imposed on the potential $V$, we study above system and obtain an infinite sequence of localized sign-changing solutions by applying the symmetric mountain pass theorem. Precisely, these solutions are constructed as higher topological type critical points of the energy functional and concentrated at a local minimum set of the potential $V$. Our method follows the same spirit of Chen and Wang’s method (Chen and Wang, 2017) which does not need any non-degeneracy condition of the limiting equations, but we cannot use it directly due to the presence of nonlocal term $\psi \left(x\right)=\frac{1}{4\pi }{\int }_{{\mathbb{R}}^3}\frac{u^2\left(y\right)}{|x-y|}dy$. We employ some new analytical skills to overcome the obstacles caused by the nonlocal term, our results improve and extend some related ones in the literature.

在本文中，我们将注意力集中在以下Schrödinger-Poisson系统上： $\left\{\begin{array}{c}-{\epsilon }^2\Delta ü+V（X）ü+\lambda \psi ü={\left|ü\right|}^{p-2}ü，X\in {\mathbb{[R}}^3，\hfill \\ -{\epsilon }^2\Delta \psi ={ü}^2，ü\in H^{\mathrm{1个}}（{\mathbb{[R}}^3）。\hfill \end{array}\right.$哪里 $4<p<6$ 和 $\epsilon ，\lambda >0$是小的正参数。在当地条件下施加潜力$V$，我们研究了上述系统，并通过应用对称山路定理获得了无限的局部符号转换解序列。精确地，这些解决方案被构造为能量功能的较高拓扑类型临界点，并集中在局部最小势能集中$V$。我们的方法遵循Chen和Wang方法（Chen and Wang，2017）的相同精神，该方法不需要限制方程的任何简并性条件，但是由于存在非局部项，因此我们不能直接使用它$\psi （X）=\frac{\mathrm{1个}}{4\pi }{\int }_{{\mathbb{[R}}^3}\frac{{ü}^2（ÿ）}{|X-ÿ|}dÿ$。我们采用了一些新的分析技能来克服非本地术语所带来的障碍，我们的结果改进并扩展了文献中的一些相关方面。