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.
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
@article{AIF_2008__58_6_2087_0, author = {Mih\u{a}ilescu, Mihai and R\u{a}dulescu, Vicen\c{t}iu}, title = {Neumann problems associated to nonhomogeneous differential operators in {Orlicz{\textendash}Sobolev} spaces}, journal = {Annales de l'Institut Fourier}, pages = {2087--2111}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {6}, year = {2008}, doi = {10.5802/aif.2407}, mrnumber = {2473630}, zbl = {1186.35065}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2407/} }
TY - JOUR AU - Mihăilescu, Mihai AU - Rădulescu, Vicenţiu TI - Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces JO - Annales de l'Institut Fourier PY - 2008 SP - 2087 EP - 2111 VL - 58 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2407/ DO - 10.5802/aif.2407 LA - en ID - AIF_2008__58_6_2087_0 ER -
%0 Journal Article %A Mihăilescu, Mihai %A Rădulescu, Vicenţiu %T Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces %J Annales de l'Institut Fourier %D 2008 %P 2087-2111 %V 58 %N 6 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2407/ %R 10.5802/aif.2407 %G en %F AIF_2008__58_6_2087_0
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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