Sign-changing solutions of critical quasilinear Kirchhoff-Schr\”{o}dinger-Poisson system with logarithmic nonlinearity

Abstract

In the present paper, we deal with the following Kirchhoff-Schr\”{o}dinger-Poisson system with logarithmic and critical nonlinearity: \begin{equation*} \begin{array}{ll} \left \{ \begin{array}{ll} \ds\B(a+b\int_\Omega|\nabla u|^2\mathrm{d}x \B)\Delta u+V(x)u-\frac{1}{2}u\Delta (u^2)+\phi u=\lambda |u|^{q-2}u\ln|u|^2+|u|^4u, &x\in \Omega, \\ -\Delta \phi=u^2,& x\in \Omega, \\ u=0,& x\in \R^3\setminus\Omega, \end{array} \right . \end{array} \end{equation*} where $\lambda,b>0,a>\frac{1}{4},4