In the present paper, we deal with the following fractional Kirchhoff–Schrödinger–Poisson system with logarithmic and critical nonlinearity: $\begin{array}{l}\left\{\begin{array}{l}(a+b[u{]}_s^2\left)\right(-\mathrm{\Delta }{)}^{s}u+V\left(x\right)u\\ +\varphi u=\lambda |u{|}^{q-2}u\ln |u{|}^2+|u{|}^{2_s^{\ast }-2}u,& x\in \mathrm{\Omega },\\ (-\mathrm{\Delta }{)}^t\varphi =u^2,& x\in \mathrm{\Omega },\\ u=0,& x\in {\mathbb{R}}^3\setminus \mathrm{\Omega },\end{array}\right.\end{array}$ where $s\in \left(\frac{3}{4},1\right),t\in (0,1),\lambda ,a,b>0,4<q<2_s^{\ast },$ and $[u{]}_s^2={\int }_{{\mathbb{R}}^3}{\int }_{{\mathbb{R}}^3}\frac{|u\left(x\right)-u\left(y\right){|}^2}{|x-y{|}^{3+2s}}\mathrm{d}x\mathrm{d}y,$ Ω is a bounded domain in ${\mathbb{R}}^3$ with Lipschitz boundary. Combining constraint variational methods, topological degree theory and quantitative deformation arguments, we prove that the above problem has a least energy sign-changing solution $u_b$. Moreover, we show that the energy of $u_b$ is strictly larger than two times the ground state energy. Finally, we regard b as a parameter and show the convergence property of $u_b$ as $b\to 0$.

在本文中，我们处理以下具有对数和临界非线性的分数阶基尔霍夫-薛定谔-泊松系统：$\begin{array}{l}\left\{\begin{array}{l}(\mathrm{一种}+b[你{]}_{秒}^{\mathrm{2个}}\left)\right(-\mathrm{△}{)}^{秒}你+V\left(X\right)你\\ +\phi 你=\lambda |你{|}^{q-\mathrm{2个}}你在|你{|}^{\mathrm{2个}}+|你{|}^{{\mathrm{2个}}_{秒}^{＊}-\mathrm{2个}}你,& X\in \mathrm{欧姆},\\ (-\mathrm{△}{)}^{吨}\phi ={你}^{\mathrm{2个}},& X\in \mathrm{欧姆},\\ 你=0,& X\in {\mathbb{R}}^{\mathrm{3个}}\setminus \mathrm{欧姆},\end{array}\right.\end{array}$在哪里$秒\in \left(\frac{\mathrm{3个}}{\mathrm{4个}},\mathrm{1个}\right),吨\in (0,\mathrm{1个}),\lambda ,\mathrm{一种},b>0,\mathrm{4个}<q<{\mathrm{2个}}_{秒}^{＊},$和$[你{]}_{秒}^{\mathrm{2个}}={\int }_{{\mathbb{R}}^{\mathrm{3个}}}{\int }_{{\mathbb{R}}^{\mathrm{3个}}}\frac{|你\left(X\right)-你\left(是\right){|}^{\mathrm{2个}}}{|X-是{|}^{\mathrm{3个}+\mathrm{2个}秒}}\mathrm{d}X\mathrm{d}是,$Ω 是一个有界域${\mathbb{R}}^{\mathrm{3个}}$与 Lipschitz 边界。结合约束变分法、拓扑度理论和定量变形论证，我们证明了上述问题具有最小能量变号解${你}_b$. 此外，我们证明了能量${你}_b$严格大于基态能量的两倍。最后，我们将b视为参数并显示收敛性${你}_b$作为$b\to 0$.