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arXiv · 0805.2529

Maximal Solutions of Semilinear Elliptic Equations with Locally Integrable Forcing Term

Moshe Marcus·Laurent Veron
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Abstract

We study the existence of a maximal solution of $-\Gd u+g(u)=f(x)$ in a domain $\Gw\subset \BBR^N$ 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 satisfies the classical $C_{1,2}$ Wiener criterion then the maximal solution is a large solution, i.e., it blows up everywhere on the boundary. In addition we discuss the question of uniqueness of large solutions.

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Moshe Marcus, Laurent Veron. 2008-05-16. Maximal Solutions of Semilinear Elliptic Equations with Locally Integrable Forcing Term. https://arxiv.org/abs/0805.2529

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