Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Uniqueness for boundary blow-up problems with continuous weights

Author(s): Jorge García-Melián
Journal: Proc. Amer. Math. Soc. 135 (2007), 2785-2793.
MSC (2000): Primary 35J25; Secondary 35J60
Posted: March 30, 2007
MathSciNet review: 2317953
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Abstract: In this paper, we prove that for the problem $\Delta u=a(x)u^p$ in a bounded domain $\Omega$ of $\mathbb{R}^N$ has a unique positive solution with $u=\infty$ on $\partial\Omega$ . The nonnegative weight 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 near $\partial\Omega$ was imposed.

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