## Differential and Integral Equations

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

#### 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

#### 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