Xian Hu, Yong-Yi Lan, Infinitely many high energy radial solutions for a Kirchhoff-Schrödinger-Poisson system, Vol. 2024 (2024), Article ID 33, pp. 1-10

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DOI: 10.23952/jnfa.2023.33

Received May 30, 2023; Accepted September 29, 2023; Published October 25, 2023

Abstract. This paper is devoted to the following Kirchhoff-Schrödinger-Poisson system
$-\bigg(a+b\int_{\mathbb{R}^{3}}|\nabla u|^{2}\,\mbox{d}x\bigg)\Delta u+u+\phi u=f(u)$ in $\mathbb{R}^{3},$
$-\Delta \phi=u^{2}$ in $\mathbb{R}^{3},$
where $a>0$ and $b\geq 0$ are two constants, and $f\in C(\mathbb{R},\mathbb{R})$ . We obtain infinitely many high energy radial solutions by using variational methods and the symmetric mountain pass lemma. The main difficulty in this paper is to obtain the boundedness of the PS-sequence. We use an extra property related to the Pohozaev identity to overcome the difficulty.

How to Cite this Article:
X. Hu, Y.Y. Lan, Infinitely many high energy radial solutions for a Kirchhoff-Schrödinger-Poisson system, J. Nonlinear Funct. Anal. 2023 (2023) 33.