Comptes Rendus
no. 9
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 Porretta1
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.

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.

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.

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

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/

[1] H. Brezis Semilinear equations in ℝN 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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