We study the following fractional Kirchhoff type equation:\begin{document}$ \begin{equation*} \begin{array}{ll} \left \{ \begin{array}{ll} \Big(a+b\int_{ \mathbb{R} ^3}|(-\Delta)^\frac{s}{2}u|^2dx\Big)(-\Delta )^s u+V(x)u = f(u)+|u|^{2^*_s-2}u, \ x\in \mathbb{R} ^3, \\ u\in H^s( \mathbb{R} ^3), \end{array} \right . \end{array} \end{equation*} $\end{document}where \begin{document}$ a, \ b>0 $\end{document} are constants, \begin{document}$ 2^*_s = \frac{6}{3-2s} $\end{document} with \begin{document}$ s\in(0, 1) $\end{document} is the critical Sobolev exponent in \begin{document}$ \mathbb{R} ^...
