  We study existence and stability of solutions of (E 1) --$\Delta$u + $\mu$
|x| 2 u + g(u) = $\nu$ in $\Omega$, u = 0 on $\partial$$\Omega$, where $\Omega$
is a bounded, smooth domain of R N , N $\ge$ 2, containing the origin, $\mu$
$\ge$ -- (N --2) 2 4 is a constant, g is a nondecreasing function satisfying
some integral growth assumption and $\nu$ is a Radon measure on $\Omega$. We
show that the situation differs according $\nu$ is diffuse or concentrated at
the origin. When g is a power we introduce a capacity framework to find
necessary and sufficient condition for solvability.
