| Titre : | Functional Differential Equations with State-Dependent Delays |
| Auteurs : | Djebli Wiam, Auteur ; DAOUDI Khelifa, Directeur de thèse |
| Type de document : | texte manuscrit |
| Editeur : | Université de Saida - Dr Moulay Tahar. Faculté des Sciences. Département de Mathématiques., 2021/2022 |
| Format : | 56p |
| Accompagnement : | CD |
| Langues: | Français |
| Index. décimale : | BUC-M 008471 |
| Catégories : | |
| Mots-clés: | Mild solution, stability, existence and uniquneness, state-dependent delays, fixed point, functional differential equations |
| Résumé : |
The objective of this thesis is to establish stability, existence, uniqueness and
model results for various classes of functional differential equations, with delay which may be finite or state-dependent in Banach space. Our results are based upon very recently fixed point theorems |
| Note de contenu : |
Contents
Introduction 7 1 Preliminaries 9 1.1 Measure of Noncompactness . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Semigroup of Linear Operator . . . . . . . . . . . . . . . . . . . . . . . 11 1.3 Some Fixed Point Theorems . . . . . . . . . . . . . . . . . . . . . . . . 19 2 Existence of Mild Solution for Neutral Functional Equations 20 2.1 Main Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3 Functional Differential Equations with State-Dependent Delays 28 3.1 Uniqueness of Mild Solutions . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2 Existence of Mild Solutions . . . . . . . . . . . . . . . . . . . . . . . . 34 4 Stability of Differential Equations with State-Dependent Delay 39 4.1 Main Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 5 Model and Application 46 5.1 A Two Body Problem of Classical Electrodynamics . . . . . . . . . . . 46 Bibliography |
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BUC-M 008471 Adobe Acrobat PDF |
