Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces
Annales de l'Institut Fourier, Volume 58 (2008) no. 6, pp. 2087-2111.

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.

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.

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
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)
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Mihăilescu, Mihai; Rădulescu, Vicenţiu. Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces. Annales de l'Institut Fourier, Volume 58 (2008) no. 6, pp. 2087-2111. doi : 10.5802/aif.2407. http://archive.numdam.org/articles/10.5802/aif.2407/

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