On démontre l'existence d'une solution positive et radialement croissante pour un problème de Neumann semilinéaire sur une boule. Aucune restriction de croissance n'est imposée sur la nonlinéarité. La méthode indroduit des contraintes de monotonie qui simplifient la preuve de l'existence d'un minimum pour la fonctionnelle associée à l'équation. Une attention particulière est consacrée à la preuve de la validité de l'équation d'Euler.
We prove the existence of a positive and radially increasing solution for a semilinear Neumann problem on a ball. No growth conditions are imposed on the nonlinearity. The method introduces monotonicity constraints which simplify the existence of a minimizer for the associated functional. Special care must be employed to establish the validity of the Euler equation.
Mots clés : Constrained variational problems, Supercritical elliptic equations, Neumann problem
@article{AIHPC_2011__28_1_63_0,
author = {Serra, Enrico and Tilli, Paolo},
title = {Monotonicity constraints and supercritical {Neumann} problems},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {63--74},
publisher = {Elsevier},
volume = {28},
number = {1},
year = {2011},
doi = {10.1016/j.anihpc.2010.10.003},
mrnumber = {2765510},
zbl = {1209.35044},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.anihpc.2010.10.003/}
}
TY - JOUR AU - Serra, Enrico AU - Tilli, Paolo TI - Monotonicity constraints and supercritical Neumann problems JO - Annales de l'I.H.P. Analyse non linéaire PY - 2011 SP - 63 EP - 74 VL - 28 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2010.10.003/ DO - 10.1016/j.anihpc.2010.10.003 LA - en ID - AIHPC_2011__28_1_63_0 ER -
%0 Journal Article %A Serra, Enrico %A Tilli, Paolo %T Monotonicity constraints and supercritical Neumann problems %J Annales de l'I.H.P. Analyse non linéaire %D 2011 %P 63-74 %V 28 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2010.10.003/ %R 10.1016/j.anihpc.2010.10.003 %G en %F AIHPC_2011__28_1_63_0
Serra, Enrico; Tilli, Paolo. Monotonicity constraints and supercritical Neumann problems. Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 1, pp. 63-74. doi : 10.1016/j.anihpc.2010.10.003. http://www.numdam.org/articles/10.1016/j.anihpc.2010.10.003/
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