In this paper, we consider the following p-Kirchhoff equation: P \( \left \{ \textstyle\begin{array}{l@{\quad}l} [M(\|u\|^{p})]^{p-1}\left (-\Delta _{p} u+|u|^{p-2}u\right )=\lambda f(x,u)+|u|^{p^{*}-2}u \quad &\mathrm{in}\ \Omega , \\ u=0,& \mathrm{on}\ \partial \Omega ,\end{array}\displaystyle \right . \) where Ω is a bounded smooth domain in ${\mathbb{R}}^{N}(N\ge 3)$ , $1< p< N$ , $\lambda >0$ , $p^{*}=\frac{Np}{N-p}$ , $M(t)$ and $f(x,t)$ are continuous functions satisfying some suitable assumptions. By using dual fountain theorem combined with concentration–compactness principle to handle the loss of compactness, we prove the existence of infinitely many solutions for system $(P)$ with nonlocal terms coupled with critical exponent.
