Large solutions of semilinear equations with Hardy potential

We consider equations of the form $-L_{\mu }u+f(u)=0$ in a smooth domain $\mathrm{\Omega }$, where $L_{\mu }=\mathrm{\Delta }+\mu {\delta }^{-2}$ 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 $(0,\mathrm{\infty })$, 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 $\mu >0$.