Sharp existence and non-existence for singular $1$-Laplace equations with Hardy potentials

In this paper, we investigate the singular Dirichlet problem \begin{equation}\label{abs1} \left\{ \begin{array}{rclr} -Δ_1u &=&\dfracλ{|x|}\hbox{Sgn}\,(u)+\dfrac{f}{u^γ}&\quad\mbox{in}\; Ω,\\[1ex] u &=&0& \quad\mbox{on}\; \partialΩ, \end{array} \right. \end{equation} where $Δ_1u=\hbox{div}\left(\f