Uniqueness of solutions of some elliptic equations without condition at infinity

Alessio Porretta

doi:10.1016/S1631-073X(02)02555-4

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 ¹

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

Comptes Rendus. Mathématique, Volume 335 (2002) no. 9, pp. 739-744.

Résumé
Abstract

On montre l'existence et l'unicité de la solution de l'équation :

- u ″ + u + {u | u' |}^{2} = f dans R, 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

R^{N}

.

We prove existence and uniqueness of solutions of the equation:

- u ″ + u + {u | u' |}^{2} = f in R, 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

R^{N}

.

Accepté le : 2002-07-22
Publié le : 2002-10-01

DOI : 10.1016/S1631-073X(02)02555-4

Affiliations des auteurs :

Alessio Porretta ¹

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

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     title = {Uniqueness of solutions of some elliptic equations without condition at infinity},
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Alessio Porretta. Uniqueness of solutions of some elliptic equations without condition at infinity. Comptes Rendus. Mathématique, Volume 335 (2002) no. 9, pp. 739-744. doi : 10.1016/S1631-073X(02)02555-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02555-4/

Bibliographie
Cité par

[1] H. Brezis Semilinear equations in $ℝ^{N}$ without condition at infinity, Appl. Math. Optim., Volume 12 (1984) no. 3, pp. 271-282

[2] J.B. Keller On solutions of Δu=f(u), Comm. Pure Appl. Math., Volume 10 (1957), pp. 503-510

[3] R. Osserman On the inequality Δu⩾f(u), Pacific J. Math., Volume 7 (1957), pp. 1641-1647

[4] A. Porretta, Local estimates and large solutions for some elliptic equations with absorption, in preparation

[5] A. Porretta, Some uniqueness results for elliptic equations without condition at infinity, Comm. Contemp. Math., to appear

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