Uniqueness for boundary blow-up problems with continuous weights

García-Melián, Jorge

doi:10.1090/S0002-9939-07-08822-3

Uniqueness for boundary blow-up problems with continuous weights
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by Jorge García-Melián PDF

Proc. Amer. Math. Soc. 135 (2007), 2785-2793 Request permission

Abstract:

In this paper, we prove that for $p>1$ the problem $\Delta u=a(x)u^p$ in a bounded $C^2$ domain $\Omega$ of $\mathbb R^N$ has a unique positive solution with $u=\infty$ on $\partial \Omega$. The nonnegative weight $a(x)$ is continuous in $\overline {\Omega }$, but is only assumed to verify a “bounded oscillations" condition of local nature near $\partial \Omega$, in contrast with previous works, where a definite behavior of $a$ near $\partial \Omega$ was imposed.

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