Ground State Solutions for Kirchhoff–Schrödinger–Poisson System with Sign-Changing Potentials

In this article, we study the following Kirchhoff–Schrödinger–Poisson system with pure power nonlinearity -(a+b∫R3|∇u|2dx)Δu+V(x)u+K(x)ϕu=h(x)|u|p-1u,x∈R3,-Δϕ=K(x)u2,x∈R3,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \left\{ \begin{array}{ll} -\Bigl (a+b \displaystyle \int _{\mathbb {R}^3}|\nabla u|^2{\text {d}}x\Bigr )\Delta u+V(x) u+K(x) \phi u= h(x)|u|^{p-1}u, &{}x\in \mathbb {R}^3, \\ -\Delta \phi =K(x)u^2, &{}x\in \mathbb {R}^3, \end{array} \right. \end{aligned}$$\end{document}where a, b are positive constants, and 3<p<5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3<p<5$$\end{document}. 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.