Concentration of positive ground state solutions for critical Kirchhoff equation with competing potentials

In this paper, we consider the following singularly perturbed Kirchhoff equation \begin{equation*} -(\varepsilon^2a+\varepsilon b\int_{$\mathbb{R}$^3}|\nabla u|^2dx)\Delta u+V(x)u=P(x)|u|^{p-2}u+Q(x)|u|^4u,\quad x\in$\mathbb{R}$^3, \end{equation*} where $\epsilon >0$ is a small parameter, $a,b>0$ are constants, $p\in (4,6)$ and $V,P,Q$ are potential functions satisfying some competing conditions. We prove the existence of a positive ground state solution by using variational methods, and we determine a concrete set related to the potentials $V,P$ and $Q$ as the concentration position of these ground state solutions as $\epsilon \to 0$.