  We present a necessary and sufficient condition on nonnegative Radon measures
$\mu$ and $\nu$ for the existence of a positive continuous solution of the
Dirichlet problem for the sublinear elliptic equation $-\Delta u=\mu u^q+\nu$
with prescribed nonnegative continuous boundary data in a general domain.
Moreover, two-sided pointwise estimates of Brezis-Kamin type for positive
bounded solutions and the uniqueness of a positive continuous $L^q$-solution
are investigated.
