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

Abstract

We study the Dirichlet problem for an elliptic equation involving the 1-Laplace operator and a reaction term, -\Delta_1 u =h(u)f(x), where f is nonnegative and h is a continuous real function that may possibly blow up at zero. We investigate optimal ranges for the data in order to obtain existence, nonexistence and (whenever expected) uniqueness of nonnegative solutions.