We are concerned with the following Kirchhoff type equation with critical nonlinearity:
$$\begin{aligned} \left\{ \begin{array}{ll} - \Bigl ( {{\varepsilon ^2}a + \varepsilon b\int _{{\mathbb {R}^3}} {{{| {\nabla u} |}^2}} } \Bigr )\Delta u + V(x)u = \lambda {| u |^{p - 2}}u + {| u |^4}u{\text { in }}{\mathbb {R}^3}, \\ u > 0,u \in {H^1}({\mathbb {R}^3}), \\ \end{array} \right. \end{aligned}$$
where
$$\varepsilon $$
is a small positive parameter,
$$a,b>0$$
,
$$\lambda > 0$$
,
$...
