Mixed local and nonlocal critical Schrodinger-Kirchhoff-Poisson type systems with logarithmic perturbation

In this article, we consider the mixed local and nonlocal critical Schrodinger-Kirchhoff-Poisson type system with logarithmic perturbation $$\displaylines{ -M(\int_{\Omega}|\nabla u|^2\,dx)\Delta u+a(-\Delta)^{s}u+\lambda\phi u =\eta |u|^{q-2}u\ln|u|^2+|u|^4u, \quad \text{in }\Omega, \cr -\Delta\phi=u^2,\quad \text{in }\Omega,\cr \phi=u=0,\quad \text{in } \mathbb{R}^3\setminus\Omega. }$$ where $\Omega\subset\mathbb{R}^3$ is a bounded domain with smooth boundary, $0<s<1$, $4<q<6$, $\lambda,\eta>0$ are two parameters, $M(t)=a+bt$ and $a,b$ are nonnegative constants. With the help of variational methods, the existence of a non-trivial ground state solution is obtained.