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 =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 .

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 .

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

[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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