Sign-changing solutions of critical quasilinear Kirchhoff-Schrödinger-Poisson system with logarithmic nonlinearity

In the present paper, we study the following Kirchhoff-Schrödinger-Poisson system with logarithmic and critical nonlinearity:

$$\begin{array}{r}\begin{array}{l}\{\begin{array}{ll}-(a+b{\int }_{\mathrm{\Omega }}|\mathrm{\nabla }u{|}^2\mathrm{d}x)\mathrm{\Delta }u+V(x)u-\frac{1}{2}u\mathrm{\Delta }(u^2)+\varphi u=\lambda |u{|}^{q-2}u\ln |u{|}^2+|u{|}^{4}u,& x\in \mathrm{\Omega },\\ -\mathrm{\Delta }\varphi =u^2,& x\in \mathrm{\Omega },\\ u=\varphi =0,& x\in \mathrm{\partial }\mathrm{\Omega },\end{array}\end{array}\end{array}$$

where $\lambda ,b>0,a>\frac{1}{4},4<q<6,$ $V(x)$ is a smooth potential function and $\mathrm{\Omega }$ is a bounded domain in ${\mathbb{R}}^3$ with Lipschitz boundary. Combining constraint variational method and perturbation method, we prove that the above problem has a least energy sign-changing solution $u_0$ which has precisely two nodal domains. Moreover, we show that the energy of $u_0$ is strictly larger than twice the ground state energy.