Comptes Rendus
Partial Differential Equations
Infinitely many solutions for a class of nonlinear eigenvalue problem in Orlicz–Sobolev spaces
[Infinité de solutions pour une classe de problèmes non linéaires de valeurs propres dans les espaces dʼOrlicz–Sobolev]
Comptes Rendus. Mathématique, Volume 349 (2011) no. 5-6, pp. 263-268.

On étudie le problème de Neumann div(α(|u|)u)+α(|u|)u=λf(x,u) dans Ω, u/ν=0 sur ∂Ω, où Ω est un domaine borné régulier de RN, λ est un paramètre positif, f est une fonction continue et α est une application définie sur (0,). Le résultat principal de cette Note montre que pour tout λ dans un certain intervalle ouvert, ce problème admet une infinité de solutions qui convergent vers zéro dans lʼespace dʼOrlicz–Sobolev W1LΦ(Ω).

We study the Neumann problem div(α(|u|)u)+α(|u|)u=λf(x,u) in Ω, u/ν=0 on ∂Ω, where Ω is a smooth bounded domain in RN, λ is a positive parameter, f is a continuous function, and α is a real-valued mapping defined on (0,). The main result in this Note establishes that for all λ in a prescribed open interval, this problem has infinitely many solutions that converge to zero in the Orlicz–Sobolev space W1LΦ(Ω).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.02.009

Gabriele Bonanno 1 ; Giovanni Molica Bisci 2 ; Vicenţiu Rădulescu 3, 4

1 Department of Science for Engineering and Architecture (Mathematics Section), Engineering Faculty, University of Messina, 98166 Messina, Italy
2 Department P.A.U., Architecture Faculty, University of Reggio Calabria, 89100 Reggio Calabria, Italy
3 Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 014700 Bucharest, Romania
4 Department of Mathematics, University of Craiova, Street A.I. Cuza No. 13, 200585 Craiova, Romania
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Gabriele Bonanno; Giovanni Molica Bisci; Vicenţiu Rădulescu. Infinitely many solutions for a class of nonlinear eigenvalue problem in Orlicz–Sobolev spaces. Comptes Rendus. Mathématique, Volume 349 (2011) no. 5-6, pp. 263-268. doi : 10.1016/j.crma.2011.02.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.02.009/

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