TABLE DES MATIÈRES Introduction............................................................................................................................5 Chapitre I. Préliminaires §1. Notations..........................................................................................................................8 §2. Mesures de non compacité..............................................................................................9 §3. Applications μ-lipschitziennes.........................................................................................11 Chapitre II. Propriétés homotopiques des applications condensantes §1. Applications essentielles et la propriété de Leray-Schauder..........................................13 §2. Théorème de transversalité topologique........................................................................15 §3. Théorème de bijection....................................................................................................17 Chapitre III. Points fixes des applications condensantes §1. Généralisations des théorèmes de point fixe.................................................................20 §2. Champs condensants....................................................................................................25 Chapitre IV. Théorie de coïncidence §1. Théorie de coïncidence pour des opérateurs de Fredholm...........................................33 §2. Remarques générales sur les applications universelles................................................38 §3. Théorie de coïncidence de Mawhin...............................................................................39 §4. Théorie de coïncidence pour des opérateurs semi-fredholmiens..................................43 Chapitre V. Applications aux équations différentielles §1. Notations........................................................................................................................47 §2. Certains résultats concernant les applications condensantes et L-condensantes.........50 §3. Applications aux équations différentielles ordinaires......................................................58 Appendices A1. Théorie du degré topologique.......................................................................................66 A2. Propriétés homotopiques de l'ensemble $GL_c(E)$.....................................................69 Commentaires.....................................................................................................................77 Références..........................................................................................................................79
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