  In this paper we deal with a Dirichlet problem for an elliptic equation
involving the $1$-Laplacian operator and a source term. We prove that, when the
growth of the source is subcritical, there exist two bounded nontrivial
solutions to our problem. Moreover, a Pohozaev type identity is proved, which
holds even when the growth is supercritical. We also show explicit examples of
our results.
