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Comptes Rendus Mathématique
Volume 339, n° 10
pages 689-694 (novembre 2004)
Doi : 10.1016/j.crma.2004.10.005
Received : 16 September 2004 ;  accepted : 22 September 2004
An extreme variation phenomenon for some nonlinear elliptic problems with boundary blow-up
Une phénomène de variation extrême pour quelque problèmes elliptiques non linéaires avec explosion au bord.
 

Florica-Corina Cîrstea 1
School of Computer Science and Mathematics, Victoria University of Technology, PO Box 14428, Melbourne, VIC 8001, Australia 

Abstract

Let be a smooth bounded domain in     and   be a non-empty open and closed subset of . Denote by   either the Dirichlet or the mixed boundary operator on   when  . We consider the nonlinear elliptic problem   in , subject to   on   when  , where a is a real number, b is a continuous non-negative function on  , while   is continuous on   such that   is increasing on  . Assuming that f varies rapidly at infinity with index (i.e.,   for all  ), we establish the uniqueness of the positive solution satisfying   on   and describe its blow-up rate via the extreme value theory. To cite this article: F.-C. Cîrstea, C. R. Acad. Sci. Paris, Ser. I 339 (2004).

The full text of this article is available in PDF format.
Résumé

Soit un domaine borné, régulier de     et   un sous-ensemble ouvert et fermé de . On désigne par   ou bien une condition de Dirichlet ou bien une condition mixte sur   si  . On étudie le problème elliptique non-linéaire   dans , avec la condition   sur   si  , où a est un réel, b est une fonction continue non-négative dans   et   est continue sur   telle que   est strictement croissante sur  . Supposons que f varie rapidement à lʼinfini dʼindex (i.e.,   pour tout  ), on établit alors lʼunicité de la solution positive avec   sur   et on décrit le taux dʼexplosion au bord en utilisant la théorie des valeurs extrêmes. Pour citer cet article : F.-C. Cîrstea, C. R. Acad. Sci. Paris, Ser. I 339 (2004).

The full text of this article is available in PDF format.
1  Supported by the Australian Government through DETYA.


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