  We establish existence and uniqueness of solution for the homogeneous
Dirichlet problem associated to a fairly general class of elliptic equations
modeled by $$
  -\Delta u= h(u){f} \ \ \text{in}\,\ \Omega, $$ where $f$ is an irregular
datum, possibly a measure, and $h$ is a continuous function that may blow up at
zero. We also provide regularity results on both the solution and the lower
order term depending on the regularity of the data, and we discuss their
optimality.
