Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 93, pp. 1-13.

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

Authors: Shengbing Deng (Southwest Univ., Chongqing, China)
         Guorong Zeng (Southwest Univ., Chongqing, China)

Abstract:
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.

Submitted August 8, 2025. Published October 06, 2025.
Math Subject Classifications: 35M12, 35R11, 35A15, 35B33.
Key Words: Ground state solution; mixed local-nonlocal operators;
 logarithmic nonlinearity; Schrodinger-Kirchhoff-Poisson system.