Differential and Integral Equations

On second-order effects in the boundary behaviour of large solutions of semilinear elliptic problems

Catherine Bandle and Moshe Marcus

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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]).

Article information

Source
Differential Integral Equations, Volume 11, Number 1 (1998), 23-34.

Dates
First available in Project Euclid: 1 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367414131

Mathematical Reviews number (MathSciNet)
MR1607972

Zentralblatt MATH identifier
1042.35535

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 34C99: None of the above, but in this section 35B40: Asymptotic behavior of solutions

Citation

Bandle, Catherine; Marcus, Moshe. On second-order effects in the boundary behaviour of large solutions of semilinear elliptic problems. Differential Integral Equations 11 (1998), no. 1, 23--34. https://projecteuclid.org/euclid.die/1367414131


Export citation