  We study existence and uniqueness of solutions of (E 1) --$\Delta$u + $\mu$
|x| ^{-2} u + g(u) = $\nu$ in $\Omega$, u = $\lambda$ on $\partial$$\Omega$,
where $\Omega$ $\subset$ R N + is a bounded smooth domain such that 0 $\in$
$\partial$$\Omega$, $\mu$ $\ge$ -- N 2 4 is a constant, g a continuous
nondecreasing function satisfying some integral growth condition and $\nu$ and
$\lambda$ two Radon measures respectively in $\Omega$ and on
$\partial$$\Omega$. We show that the situation differs considerably according
the measure is concentrated at 0 or not. When g is a power we introduce a
capacity framework which provides necessary and sufficient conditions for the
solvability of problem (E 1).
