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Comptes Rendus Mathématique
Volume 335, n° 9
pages 739-744 (novembre 2002)
Doi : S1631-073X(02)02555-4
accepted : 22 July 2002
Uniqueness of solutions of some elliptic equations without condition at infinity
Unicité de la solution de certaines équations elliptiques sans conditions à l'infini
 

Alessio Porretta
Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italy 

Note presented by Haïm Brézis

Abstract

We prove existence and uniqueness of solutions of the equation: −u″+u+u|u′|2=finR,f⩾0, without any condition at infinity on f . The result is generalized to other absorbing equations of the same type and to the radial case in RN. To cite this article: A. Porretta, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 739-744.

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

On montre l'existence et l'unicité de la solution de l'équation : −u″+u+u|u′|2=fdansR,f⩾0, sans conditions à l'infini sur f . Le résultat admet des généralisations à d'autres equations avec termes d'absorption du même type et au cas radial dans RN. Pour citer cet article : A. Porretta, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 739-744.

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


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