Singularities for a 2-Dimensional Semilinear Elliptic Equation with a Non-Lipschitz Nonlinearity

We study the limit behaviour of solutions of the semilinear elliptic equationΔu=|x|σ|u|q−1uinR2,q∈(0, 1),σ∈R,with a non-Lipschitz nonlinearity on the right-hand side. When |σ+2|⩽2 we give a complete classification of the types of singularities asx→0 andx→∞ which in the rescaled form are essentially...

Full description

Saved in:
Bibliographic Details
Published in:Journal of Differential Equations 1999-05, Vol.154 (2), p.318-338
Main Authors: Bidaut-Véron, Marie-Francoise, Galaktionov, Victor, Grillot, Philippe, Véron, Laurent
Format: Article
Language:English
Subjects:
asymptotics of singularities
semilinear elliptic equation
Sturmian argument
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study the limit behaviour of solutions of the semilinear elliptic equationΔu=|x|σ|u|q−1uinR2,q∈(0, 1),σ∈R,with a non-Lipschitz nonlinearity on the right-hand side. When |σ+2|⩽2 we give a complete classification of the types of singularities asx→0 andx→∞ which in the rescaled form are essentially non-analytic and, even more, notC∞. The proof is based on the asymptotic study of the corresponding evolution dynamical system and the Sturmian argument on zero set analysis.
ISSN:0022-0396
1090-2732
DOI:10.1006/jdeq.1998.3567