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

Abstract

In this article, we study the following Kirchhoff–Schrodinger–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.