  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
$\varepsilon>0$ 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
$\varepsilon\to0$.
