Least-energy sign-changing solutions for Kirchhoff–Schrödinger–Poisson systems in R 3 $\mathbb{R}^{3}$

In this paper, we study the following Kirchhoff–Schrödinger–Poisson systems: $$\textstyle\begin{cases} -(a+b\int _{\mathbb{R}^{3}} \vert \nabla u \vert ^{2}\,dx)\Delta u+V(x)u+\phi u=f(u), &x \in \mathbb{R}^{3}, \\ -\Delta \phi =u^{2}, &x\in \mathbb{R}^{3}, \end{cases} $$ where a, b are positive constants, $V\in \mathcal{C}(\mathbb{R} ^{3},\mathbb{R}^{+})$ . By using constraint variational method and the quantitative deformation lemma, we obtain a least-energy sign-changing (or nodal) solution $u_{b}$ to this problem, and study the energy property of $u_{b}$ . Moreover, we investigate the asymptotic behavior of $u_{b}$ as the parameter ${b\searrow 0}$ .