Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1042.35535
Bandle, Catherine; Marcus, Moshe
On second-order effects in the boundary behaviour of large solutions of semilinear elliptic problems. (English)
[J] Differ. Integral Equ. 11, No. 1, 23-34 (1998). ISSN 0893-4983

Let $D$ be a bounded smooth domain in $\Bbb R^N$. 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 the authors consider a secondary effect in the asymptotic behaviour of solutions, namely, the behaviour of $u/\phi (\delta ) - 1$ as $\delta \rightarrow 0$. They derive estimates for this expression, which are valid for a large class of nonlinearities and extend a recent result of Lazer and McKenna.
[Pavel Drábek (Plzeň)]

MSC 2000:: *35J60 Nonlinear elliptic equations
34C99 Qualitative theory of solutions of ODE
35B40 Asymptotic behavior of solutions of PDE

Cited in: Zbl 1129.35312

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]