  We study the existence of nonnegative solutions to the Dirichlet problem
$\CL^{_{^M}}_{p,q}u:=-\Delta u+u^p-M|\nabla u|^q=\mu$ in a domain
$\Omega\subset\BBR^N$ where $\mu$ is a nonnegative Radon measure, when $p>1$,
$q>1$ and $M\geq 0$. We also give conditions under which nonnegative solutions
of $\CL^{_{^M}}_{p,q}u=0$ in $\Omega\setminus K$ where $K$ is a compact subset
of $\Omega$ can be extended as a solution of the same equation in $\Omega$
