Mihăilescu, Mihai; Rădulescu, Vicenţiu
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 ]
Annales de l'institut Fourier, Tome 58 (2008) no. 6 , p. 2087-2111
Zbl 1186.35065 | MR 2473630 | Zbl pre05367570
doi : 10.5802/aif.2407
URL stable : http://www.numdam.org/item?id=AIF_2008__58_6_2087_0

Classification:  35D05,  35J60,  35J70,  58E05,  68T40,  76A02
Mots clés: opérateur différentiel non homogène, équation aux dérivées partielles non linéaire, problème de Neumann, espace d’Orlicz–Sobolev
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.

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