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1998 On second-order effects in the boundary behaviour of large solutions of semilinear elliptic problems
Catherine Bandle, Moshe Marcus
Differential Integral Equations 11(1): 23-34 (1998).

Abstract

Let $D$ be a bounded smooth domain in $\mathbb{R}^N$. It is well known that large solutions of an equation such as $\Delta u= u^p, \;p>1$ in $D$ blow up at the boundary at a rate $\phi(\delta)$ which depends only on $p$. (Here $\delta(x)$ denotes the distance of $x$ to the boundary.) In this paper we consider a secondary effect in the asymptotic behaviour of solutions, namely, the behaviour of $u/\phi(\delta)-1$ as $\delta \to 0$. We derive estimates for this expression, which are valid for a large class of nonlinearities and extend a recent result of Lazer and McKenna ([7]).

Citation

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Catherine Bandle. Moshe Marcus. "On second-order effects in the boundary behaviour of large solutions of semilinear elliptic problems." Differential Integral Equations 11 (1) 23 - 34, 1998.

Information

Published: 1998
First available in Project Euclid: 1 May 2013

zbMATH: 1042.35535
MathSciNet: MR1607972

Subjects:
Primary: 35J60
Secondary: 34C99, 35B40

Rights: Copyright © 1998 Khayyam Publishing, Inc.

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Vol.11 • No. 1 • 1998
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