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)^{σ-1}(-Δ)^s_p u = \fracλ{u^γ}+u^{ p_s^{}-1 }\quad $\text{in }$Ω,\ u>0,;;;;\quad $\text{in }$Ω,\ u=0,;;;;\quad $\text{in }$$\mathbb{R}$^{N}\setminus Ω,\end{array} \right. \end{equation} where $\mathrm{\Omega }$ is a bounded domain in ${\mathbb{R}}^N$ with the smooth boundary $\mathrm{\partial }\mathrm{\Omega }$, $0<s<1<p<\mathrm{\infty }$, $N>sp$, $1<\sigma <p_s^{\ast }\mathrm{/}p,$ with $p_s^{\ast }=\frac{Np}{N-ps},$ $(-\mathrm{\Delta }{)}_p^s$ is the nonlocal $p$-Laplace operator and $[u{]}_{s,p}$ is the Gagliardo $p$-seminorm. We combine some variational techniques with a truncation argument in order to show the existence and the multiplicity of positive solutions to the above problem.