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Etude des valeurs propres et de la résonance pour l’opérateur p-Laplacien

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Author(s): A. Anane
Series: Thése de doctorat
Publisher: Université Libre de Bruxelles
Year: 1988

Language: French
Pages: 110
City: Brussels

TABLE DE MATIERES
0 - RAPPELS ET NOTATIONS GENERALES ------------------------------------------------- 2
PREMIERE PARTIE : VALEURS PROPRES ET FONCTIONS PROPRES DU p-LAPLACIEN
1 - INTRODUCTION ET NOTATIONS---- -------------------------------------------------- 6
2 - EXISTENCE D'UNE INFINITE DE VALEURS PROPRES ------------------------------------ 10
3 - SUR LA PREMIERE VALEUR PROPRE -------------------------------------------------- 17
h - CAS DE LA BOULE UNITE ---------------------------------------------------------- 26
DEUXIEME PARTIE : RESONANCE ET NON-RESONANCE POUR LE p-LAPLACIEN ET GENERALISATION
I - INTRODUCTION ET PRELIMINAIRES -------------------------------------------------- 41
II - PROBLEMES NON RESONANTS ------------------------------------------------------- 47
III - PROBLEMES AVEC RESONANCE ----------------------------------------------------- 61
IV - GENERALISATION ---------------------------------------------------------------- 79
ANNEXE : ESTIMATIONS L^infiniy(Omega) ---------------------------------------------- 96