In this article, we study the following Kirchhoff–Schrödinger–Poisson system with pure power nonlinearity

$$\begin{aligned} \left\{ \begin{array}{ll} -\Bigl (a+b \displaystyle \int _{\mathbb {R}^3}|\nabla u|^2{\text {d}}x\Bigr )\Delta u+V(x) u+K(x) \phi u= h(x)|u|^{p-1}u, &{}x\in \mathbb {R}^3, \\ -\Delta \phi =K(x)u^2, &{}x\in \mathbb {R}^3, \end{array} \right. \end{aligned}$$

where a, b are positive constants, and \(3<p<5\). Under some proper assumptions on the potentials V, K and h, not requiring nonnegative property, we find a ground state solution for the above problem with the help of Nehari manifold.

中文翻译：

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具有符号改变电势的基尔霍夫–薛定ding–泊松系统的基态解决方案

在本文中，我们研究以下具有纯功率非线性的Kirchhoff–Schrödinger–Poisson系统

$$ \ begin {aligned} \ left \ {\ begin {array} {ll}-\ Bigl（a + b \ displaystyle \ int _ {\ mathbb {R} ^ 3} | \ nabla u | ^ 2 {\ text {d}} x \ Bigr）\ Delta u + V（x）u + K（x）\ phi u = h（x）| u | ^ {p-1} u，＆{} x \ in \ mathbb { R} ^ 3，\\-\ Delta \ phi = K（x）u ^ 2，＆{} x \在\ mathbb {R} ^ 3，\ end {array} \ right中。\ end {aligned} $$

其中a，  b是正常数，和\（3 <p <5 \）。在对电位V，K和h的一些适当假设下，不需要非负性质，我们借助Nehari流形为上述问题找到了基态解。