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.
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Nikolaos S. Papageorgiou 1 ; Vicenţiu D. Rădulescu 2, 3
@article{CRMATH_2014__352_10_811_0, author = {Nikolaos S. Papageorgiou and Vicen\c{t}iu D. R\u{a}dulescu}, 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}, }
TY - JOUR AU - Nikolaos S. Papageorgiou AU - Vicenţiu D. Rădulescu 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 DO - 10.1016/j.crma.2014.08.009 LA - en ID - CRMATH_2014__352_10_811_0 ER -
%0 Journal Article %A Nikolaos S. Papageorgiou %A Vicenţiu D. Rădulescu %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 %R 10.1016/j.crma.2014.08.009 %G en %F CRMATH_2014__352_10_811_0
Nikolaos S. Papageorgiou; Vicenţiu D. Rădulescu. Bifurcation near infinity for the Neumann problem with concave–convex nonlinearities. Comptes Rendus. Mathématique, Volume 352 (2014) no. 10, pp. 811-816. doi : 10.1016/j.crma.2014.08.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.08.009/
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