The Dirichlet problem for the 1-Laplacian with a general singular term and L ¹-data

We study the Dirichlet problem for an elliptic equation involving $1$-Laplace operator and a reaction term, namely: $$ \left\{\begin{array}{ll} \displaystyle -\Delta_1 u =h(u)f(x)&\hbox{in }\Omega\,,\\ u=0&\hbox{on }\partial\Omega\,, \end{array}\right. where $ \Omega \subset \mathbb{R}^N$ is open bounded set having Lipschitz boundary, $f\in L^1(\Omega)$ nonnegative, $h$ continuous real function that may possibly blow up at zero. investigate optimal ranges data in order to obtain existence, nonexistence (whenever expected) uniqueness of nonnegative solutions.