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Comptes Rendus Mathématique
Volume 341, n° 4
pages 239-242 (août 2005)
Doi : 10.1016/j.crma.2005.06.036
Received : 9 June 2005 ;  accepted : 25 June 2005
Une méthode des sur et sous solutions améliorée
An improved upper and lower solutions method

Philippe Delanoë 1
Université de Nice-Sophia Antipolis, laboratoire J.-A. Dieudonné, parc Valrose, 06108 Nice cedex 2, France 


Lʼhabituelle méthode des sur et sous solutions, pour résoudre une équation non-linéaire elliptique du second ordre, est itérative, ce qui complique, parfois jusquʼà la rendre impossible, lʼindispensable estimation uniforme  , à cause de la présence simultanée de deux inconnues successives de lʼitération dans la même équation. Nous présentons ici une méthode dépourvue de cet inconvénient, basée sur un argument de point fixe élémentaire. Pour citer cet article : P. Delanoë, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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

The usual upper and lower solutions method for solving a second order nonlinear elliptic equation is iterative, with the drawback of a tricky, if not sometimes impossible, derivation of the (quite essential) uniform   estimate, due to the occurence in the same equation of two successive iteration unknowns. We present here a method free of such a drawback, based on an elementary fixed point argument. To cite this article: P. Delanoë, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.
1  Supported by the CNRS.

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