Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces

Mihăilescu, Mihai; Rădulescu, Vicenţiu

doi:10.5802/aif.2407

Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces
[Problèmes de Neumann associés aux opérateurs différentiels non homogènes dans les espaces d’Orlicz–Sobolev]

Mihăilescu, Mihai ¹ ; Rădulescu, Vicenţiu ²

¹ University of Craiova Department of Mathematics 200585 Craiova (Romania) Central European University Department of Mathematics 1051 Budapest (Hungary)
² Institute of Mathematics “Simion Stoilow” of the Romanian Academy P.O. Box 1-764 014700 Bucharest (Romania) University of Craiova Department of Mathematics 200585 Craiova (Romania)

Annales de l'Institut Fourier, Tome 58 (2008) no. 6, pp. 2087-2111.

Résumé
Abstract

On étudie un problème aux limites de Neumann associé à un opérateur différentiel non homogène. En tenant compte de la compétition entre le taux de croissance de la nonlinéarité et les valeurs du paramètre de bifurcation, on établit des conditions suffisantes pour l’existence de solutions non triviales dans un certain espace fonctionnel du type Orlicz–Sobolev.

We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the existence of nontrivial solutions in a related Orlicz–Sobolev space.

EuDML MR Zbl

DOI : 10.5802/aif.2407

Classification : 35D05, 35J60, 35J70, 58E05, 68T40, 76A02
Keywords: Nonhomogeneous differential operator, nonlinear partial differential equation, Neumann boundary value problem, Orlicz–Sobolev space
Mot clés : opérateur différentiel non homogène, équation aux dérivées partielles non linéaire, problème de Neumann, espace d’Orlicz–Sobolev

Affiliations des auteurs :

Mihăilescu, Mihai ¹ ; Rădulescu, Vicenţiu ²

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     title = {Neumann problems associated to nonhomogeneous differential operators in {Orlicz{\textendash}Sobolev} spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {2087--2111},
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Mihăilescu, Mihai; Rădulescu, Vicenţiu. Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces. Annales de l'Institut Fourier, Tome 58 (2008) no. 6, pp. 2087-2111. doi : 10.5802/aif.2407. http://www.numdam.org/articles/10.5802/aif.2407/

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