[Bifurcation autour de l'origine pour le problème de Robin avec terme concave–convexe]
Dans cette Note, nous étudions le problème elliptique paramétrique de Robin pour un opérateur différentiel non homogène et avec une réaction qui présente des termes concurrents (du type concave–convexe). Sans utiliser la condition d'Ambrosetti–Rabinowitz, nous prouvons un théorème de bifurcation pour de petites valeurs positives du paramètre réel.
In this Note, we deal with the Robin parametric elliptic equation driven by a nonhomogeneous differential operator and with a reaction that exhibits competing terms (concave–convex nonlinearities). Without employing the Ambrosetti–Rabinowitz condition, we prove a bifurcation theorem for small positive values of the real parameter.
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@article{CRMATH_2014__352_7-8_627_0,
author = {Papageorgiou, Nikolaos S. and R\u{a}dulescu, Vicen\c{t}iu D.},
title = {Bifurcation near the origin for the {Robin} problem with concave{\textendash}convex nonlinearities},
journal = {Comptes Rendus. Math\'ematique},
pages = {627--632},
publisher = {Elsevier},
volume = {352},
number = {7-8},
year = {2014},
doi = {10.1016/j.crma.2014.05.007},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2014.05.007/}
}
TY - JOUR AU - Papageorgiou, Nikolaos S. AU - Rădulescu, Vicenţiu D. TI - Bifurcation near the origin for the Robin problem with concave–convex nonlinearities JO - Comptes Rendus. Mathématique PY - 2014 SP - 627 EP - 632 VL - 352 IS - 7-8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.05.007/ DO - 10.1016/j.crma.2014.05.007 LA - en ID - CRMATH_2014__352_7-8_627_0 ER -
%0 Journal Article %A Papageorgiou, Nikolaos S. %A Rădulescu, Vicenţiu D. %T Bifurcation near the origin for the Robin problem with concave–convex nonlinearities %J Comptes Rendus. Mathématique %D 2014 %P 627-632 %V 352 %N 7-8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2014.05.007/ %R 10.1016/j.crma.2014.05.007 %G en %F CRMATH_2014__352_7-8_627_0
Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D. Bifurcation near the origin for the Robin problem with concave–convex nonlinearities. Comptes Rendus. Mathématique, Tome 352 (2014) no. 7-8, pp. 627-632. doi : 10.1016/j.crma.2014.05.007. http://www.numdam.org/articles/10.1016/j.crma.2014.05.007/
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