Nonlocal p-Kirchhoff equations with singular and critical nonlinearity terms

The objective of this work is to investigate a nonlocal problem involving singular and critical nonlinearities:\begin{equation*}\left\{\begin{array}{ll} ([u]_{s,p}^p)^{\sigma-1}(-\Delta)^s_p u = \frac{\lambda}{u^{\gamma}}+u^{ p_s^{*}-1 }\quad \text{in }\Omega,\\ u>0,\;\;\;\;\quad u=0,\;\;\;\;\quad }\mathbb{R}^{N}\setminus \Omega,\end{array} \right. \end{equation*} where $\Omega$ bounded domain in $\mathbb{R}^N$ with the smooth boundary $\partial \Omega$, $0 < s< 1 sp$, $1<\sigma<p^*_s/p,$ $p_s^{*}=\frac{Np}{N-ps},$ $ (- \Delta )_p^s$ $p$-Laplace operator $[u]_{s,p}$ Gagliardo $p$-seminorm. We combine some variational techniques truncation argument order show existence multiplicity positive solutions above problem.