  We consider equations of the form $-L_\mu u +f(u)=0$ in a smooth domain
$\Omega$, where $L_\mu=\Delta + \mu\delta^{-2}$ and $\delta(x)$ denotes the
distance of the point $x$ to the boundary of the domain. The nonlinear term $f$
is positive, increasing and convex on $(0,\infty)$, satisfies the
Keller-Osserman condition and some additional technical assumptions. The
conditions are satisfied, in particular, by power and exponential
nonlinearities. We discuss the question of existence and uniqueness of large
solutions when $\mu>0$.
