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ESAIM: Proc., 2007, Vol. 20, pp. 53-62
DOI: 10.1051/proc:072005
Existence of nontrivial solutions for quasi-linear resonant problems
Abdesslem AYOUJIL and Abdel Rachid El AMROUSSDepartment of Mathematics, Faculty of Sciences, University Mohammed I, Oujda, Morocco
abayoujil@yahoo.fr
amrouss@sciences.univ-oujda.ac.ma
(Published online: 13 October 2007)
Abstract
Combining the
minimax arguments and the Morse Theory, by computing the critical
groups at zero, we establish the existence of a nontrivial solution
for a class of Dirichlet boundary value problems, with resonance at
infinity and zero.
Résumé
Par un procédé de minimax et application de la Théorie de
Morse, en calculant les groupes critiques en zéro, nous
établissons l'existence d'une solution non triviale pour une
classe de problèmes de Dirichlet, avec résonance à l'infini et
en zéro..
Mathematics Subject Classification. 58E05, 35J65, 49B27
Key words: minimax method, p-Laplacian , resonance elliptic equation, critical group, Morse theory,
© EDP Sciences, ESAIM 2007
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