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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematical Sciences, TianGong University, Tianjin, 300387, China

    Ying Wang & Ziheng Zhang

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  1. Ying Wang
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  2. Ziheng Zhang
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Correspondence to Ziheng Zhang.

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Communicated by Rosihan M. Ali.

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Project supported by the National Natural Science Foundation of China (Grant No.11771044).

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Wang, Y., Zhang, Z. Ground State Solutions for Kirchhoff–Schrödinger–Poisson System with Sign-Changing Potentials. Bull. Malays. Math. Sci. Soc. 44, 2319–2333 (2021). https://doi.org/10.1007/s40840-020-01061-z

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  • DOI: https://doi.org/10.1007/s40840-020-01061-z

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