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We study the existence of a maximal solution of $-\Gd u+g(u)=f(x)$ in adomain $\Gw\subset \BBR^N$ with compact boundary, assuming that $f\in(L^1_{loc}(\Gw))_+$ and that $g$ is nondecreasing, $g(0)\geq 0$ and $g$satisfies the Keller-Osserman condition. We show that if the boundary satisfiesthe classical $C_{1,2}$ Wiener criterion then the maximal solution is a largesolution, i.e., it blows up everywhere on the boundary. In addition we discussthe question of uniqueness of large solutions.

Maximal Solutions of Semilinear Elliptic Equations with Locally Integrable Forcing Term