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Comptes Rendus Mathématique
Volume 336, n° 9
pages 725-730 (mai 2003)
Doi : 10.1016/S1631-073X(03)00129-8
Received : 18 November 2002 ;  accepted : 4 February 2003
Sur les équations de Lane-Emden avec opérateurs non linéaires
On the Lane-Emden equations with fully nonlinear operators

Isabeau  Birindelli,  Françoise  Demengel
Département de mathématiques, Université de Cergy-Pontoise, site Saint-Martin, PB 222, 95302 Cergy-Pontoise cedex, France 

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Dans cette Note on considère les solutions non négatives de l'équation non linéaire   dans  , et   est l'opérateur de Pucci   où les   sont les valeurs propres de   et  . On montre que si   vérifie une hypothèse de décroissance à l'infini   avec  , alors   est radiale. Dans un deuxième temps on montre que si  , toute solution radiale de (1),  , telle que   ne change de signe qu'une seule fois, est nulle. Pour citer cet article : I. Birindelli, F. Demengel, C. R. Acad. Sci. Paris, Ser. I 336 (2003).

Abstract

In this Note we consider nonnegative solutions for the nonlinear equation   in  , where   is the so called Pucci operator   and the   are the eigenvalues of   et  . We prove that if   satisfies the decreasing estimate   for some   satisfying   then   is radial. In a second time we prove that if   and   is a nonnegative radial solution of (1),  , such that   changes sign at most once, then   is zero. To cite this article: I. Birindelli, F. Demengel, C. R. Acad. Sci. Paris, Ser. I 336 (2003).




© 2003  Académie des sciences@@#104156@@

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