[Bifurcation à l'infini pour le problème de Neumann avec terme concave–convexe]
Dans cette Note, nous étudions le problème elliptique paramétrique de Neumann pour un opérateur différentiel non homogène et avec une réaction qui présente des termes du type concave–convexe. En utilisant la condition d'Ambrosetti–Rabinowitz en combinaison avec des outils topologiques et variationnels, nous prouvons un théorème de bifurcation pour de grandes valeurs du paramètre réel.
In this Note, we study a class of Neumann parametric elliptic equations driven by a nonhomogeneous differential operator and with a reaction that exhibits competing terms (concave–convex nonlinearities). Using the Ambrosetti–Rabinowitz condition and related topological and variational arguments, we prove a bifurcation result for large values of the parameter.
Accepté le :
Publié le :
@article{CRMATH_2014__352_10_811_0,
author = {Papageorgiou, Nikolaos S. and R\u{a}dulescu, Vicen\c{t}iu D.},
title = {Bifurcation near infinity for the {Neumann} problem with concave{\textendash}convex nonlinearities},
journal = {Comptes Rendus. Math\'ematique},
pages = {811--816},
publisher = {Elsevier},
volume = {352},
number = {10},
year = {2014},
doi = {10.1016/j.crma.2014.08.009},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2014.08.009/}
}
TY - JOUR AU - Papageorgiou, Nikolaos S. AU - Rădulescu, Vicenţiu D. TI - Bifurcation near infinity for the Neumann problem with concave–convex nonlinearities JO - Comptes Rendus. Mathématique PY - 2014 SP - 811 EP - 816 VL - 352 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.08.009/ DO - 10.1016/j.crma.2014.08.009 LA - en ID - CRMATH_2014__352_10_811_0 ER -
%0 Journal Article %A Papageorgiou, Nikolaos S. %A Rădulescu, Vicenţiu D. %T Bifurcation near infinity for the Neumann problem with concave–convex nonlinearities %J Comptes Rendus. Mathématique %D 2014 %P 811-816 %V 352 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2014.08.009/ %R 10.1016/j.crma.2014.08.009 %G en %F CRMATH_2014__352_10_811_0
Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D. Bifurcation near infinity for the Neumann problem with concave–convex nonlinearities. Comptes Rendus. Mathématique, Tome 352 (2014) no. 10, pp. 811-816. doi : 10.1016/j.crma.2014.08.009. http://www.numdam.org/articles/10.1016/j.crma.2014.08.009/
[1] Dual variational methods in critical point theory and applications, J. Funct. Anal., Volume 14 (1973), pp. 349-381
[2] Combined effects of concave–convex nonlinearities in some elliptic problems, J. Funct. Anal., Volume 122 (1994), pp. 519-543
[3] Linear and Nonlinear Functional Analysis with Applications, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, USA, 2013
[4] The natural generalization of the conditions of Ladyzhenskaya and Uraltseva for elliptic equations, Commun. Partial Differ. Equ., Volume 16 (1991), pp. 311-361
[5] Positive solutions to a Dirichlet problem with p-Laplacian and concave–convex nonlinearity depending on a parameter, Commun. Pure Appl. Anal., Volume 12 (2013), pp. 815-829
[6] N.S. Papageorgiou, V.D. Rădulescu, Bifurcation of positive solutions for nonlinear nonhomogeneous Robin and Neumann problems with competing nonlinearities, submitted for publication.
[7] The Maximum Principle, Birkhäuser, Basel, Switzerland, 2007
Cité par Sources :
