Large solutions of semilinear equations with Hardy potential

We consider equations of the form $-L_μu +f(u)=0$ in a smooth domain $Ω$, where $L_μ=Δ+ μδ^{-2}$ and $δ(x)$ 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 $μ>0$.

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