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Introduction To Functional Differential Equations

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Introduction To Functional Differential Equations

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Author : Jack K. Hale
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-10-14

Introduction To Functional Differential Equations written by Jack K. Hale and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-14 with Mathematics categories.

The present book builds upon an earlier work of J. Hale, "Theory of Func tional Differential Equations" published in 1977. We have tried to maintain the spirit of that book and have retained approximately one-third of the material intact. One major change was a complete new presentation of lin ear systems (Chapters 6~9) for retarded and neutral functional differential equations. The theory of dissipative systems (Chapter 4) and global at tractors was completely revamped as well as the invariant manifold theory (Chapter 10) near equilibrium points and periodic orbits. A more complete theory of neutral equations is presented (see Chapters 1, 2, 3, 9, and 10). Chapter 12 is completely new and contains a guide to active topics of re search. In the sections on supplementary remarks, we have included many references to recent literature, but, of course, not nearly all, because the subject is so extensive. Jack K. Hale Sjoerd M. Verduyn Lunel Contents Preface............................................................ v Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . 1. Linear differential difference equations . . . . . . . . . . . . . . 11 . . . . . . 1.1 Differential and difference equations. . . . . . . . . . . . . . . . . . . . 11 . . . . . . . . 1.2 Retarded differential difference equations. . . . . . . . . . . . . . . . 13 . . . . . . . 1.3 Exponential estimates of x( ¢,f) . . . . . . . . . . . . . . . . . . . . . 15 . . . . . . . . . . 1.4 The characteristic equation . . . . . . . . . . . . . . . . . . . . . . . . 17 . . . . . . . . . . . . 1.5 The fundamental solution. . . . . . . . . . . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . 1.6 The variation-of-constants formula............................. 23 1. 7 Neutral differential difference equations . . . . . . . . . . . . . . . . . 25 . . . . . . . 1.8 Supplementary remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . 34 . . . . . . . . . . . . . 2. Functional differential equations: Basic theory . . . . . . . . 38 . . 2.1 Definition of a retarded equation. . . . . . . . . . . . . . . . . . . . . . 38 . . . . . . . . . 2.2 Existence, uniqueness, and continuous dependence . . . . . . . . . . 39 . . . 2.3 Continuation of solutions . . . . . . . . . . . . . . . . . . . . . . . . . . 44 . . . . . . . . . . . .

Introduction To Functional Differential Equations

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Author : Jack K. Hale
language : en
Publisher:
Release Date : 2014-09-01

Introduction To Functional Differential Equations written by Jack K. Hale and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.

Introduction To Functional Differential Equations

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Author : Jack K. Hale
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21

The present book builds upon an earlier work of J. Hale, "Theory of Func tional Differential Equations" published in 1977. We have tried to maintain the spirit of that book and have retained approximately one-third of the material intact. One major change was a complete new presentation of lin ear systems (Chapters 6~9) for retarded and neutral functional differential equations. The theory of dissipative systems (Chapter 4) and global at tractors was completely revamped as well as the invariant manifold theory (Chapter 10) near equilibrium points and periodic orbits. A more complete theory of neutral equations is presented (see Chapters 1, 2, 3, 9, and 10). Chapter 12 is completely new and contains a guide to active topics of re search. In the sections on supplementary remarks, we have included many references to recent literature, but, of course, not nearly all, because the subject is so extensive. Jack K. Hale Sjoerd M. Verduyn Lunel Contents Preface............................................................ v Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . 1. Linear differential difference equations . . . . . . . . . . . . . . 11 . . . . . . 1.1 Differential and difference equations. . . . . . . . . . . . . . . . . . . . 11 . . . . . . . . 1.2 Retarded differential difference equations. . . . . . . . . . . . . . . . 13 . . . . . . . 1.3 Exponential estimates of x( ¢,f) . . . . . . . . . . . . . . . . . . . . . 15 . . . . . . . . . . 1.4 The characteristic equation . . . . . . . . . . . . . . . . . . . . . . . . 17 . . . . . . . . . . . . 1.5 The fundamental solution. . . . . . . . . . . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . 1.6 The variation-of-constantsformula............................. 23 1. 7 Neutral differential difference equations . . . . . . . . . . . . . . . . . 25 . . . . . . . 1.8 Supplementary remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . 34 . . . . . . . . . . . . . 2. Functional differential equations: Basic theory . . . . . . . . 38 . . 2.1 Definition of a retarded equation. . . . . . . . . . . . . . . . . . . . . . 38 . . . . . . . . . 2.2 Existence, uniqueness, and continuous dependence . . . . . . . . . . 39 . . . 2.3 Continuation of solutions . . . . . . . . . . . . . . . . . . . . . . . . . . 44 . . . . . . . . . . . .

Functional Differential Equations

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Author :
language : en
Publisher:
Release Date : 1994

Functional Differential Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.

Functional Differential Equations

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Author : Jack K. Hale
language : en
Publisher:
Release Date : 1971-05-14

Functional Differential Equations written by Jack K. Hale and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-05-14 with categories.

The book is an introduction to functional differential equations based on a series of lectures given by the author at UCLA during the Applied Mathematics year 1968-1969. The interest here is on a geometric theory of FDE. In particular the equations of the retarded types are considered. (Author).

Introduction To The Theory Of Functional Differential Equations Methods And Applications

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Author : Nikolaj Viktorovič Azbelev
language : en
Publisher: Hindawi Publishing Corporation
Release Date : 2007

Introduction To The Theory Of Functional Differential Equations Methods And Applications written by Nikolaj Viktorovič Azbelev and has been published by Hindawi Publishing Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Electronic books categories.

Bifurcation Theory Of Functional Differential Equations

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Author : Shangjiang Guo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-30

Bifurcation Theory Of Functional Differential Equations written by Shangjiang Guo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-30 with Mathematics categories.

This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering and the study of FDEs has been a major source of inspiration for advancement in nonlinear analysis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and frameworks for the investigation of bifurcation phenomena of FDEs depending on parameters with chap. This well illustrated book aims to be self contained so the readers will find in this book all relevant materials in bifurcation, dynamical systems with symmetry, functional differential equations, normal forms and center manifold reduction. This material was used in graduate courses on functional differential equations at Hunan University (China) and York University (Canada).

Functional Differential Equations

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Author : A.V. Kim
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Functional Differential Equations written by A.V. Kim and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

Beginning with the works of N.N.Krasovskii [81, 82, 83], which clari fied the functional nature of systems with delays, the functional approach provides a foundation for a complete theory of differential equations with delays. Based on the functional approach, different aspects of time-delay system theory have been developed with almost the same completeness as the corresponding field of ODE (ordinary differential equations) the ory. The term functional differential equations (FDE) is used as a syn onym for systems with delays 1. The systematic presentation of these re sults and further references can be found in a number of excellent books [2, 15, 22, 32, 34, 38, 41, 45, 50, 52, 77, 78, 81, 93, 102, 128]. In this monograph we present basic facts of i-smooth calculus ~ a new differential calculus of nonlinear functionals, based on the notion of the invariant derivative, and some of its applications to the qualitative theory of functional differential equations. Utilization of the new calculus is the main distinction of this book from other books devoted to FDE theory. Two other distinguishing features of the volume are the following: - the central concept that we use is the separation of finite dimensional and infinite dimensional components in the structures of FDE and functionals; - we use the conditional representation of functional differential equa tions, which is convenient for application of methods and constructions of i~smooth calculus to FDE theory.

Introduction To The Theory And Applications Of Functional Differential Equations

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Author : V. Kolmanovskii
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18

Introduction To The Theory And Applications Of Functional Differential Equations written by V. Kolmanovskii and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.

This book covers the most important issues in the theory of functional differential equations and their applications for both deterministic and stochastic cases. Among the subjects treated are qualitative theory, stability, periodic solutions, optimal control and estimation, the theory of linear equations, and basic principles of mathematical modelling. The work, which treats many concrete problems in detail, gives a good overview of the entire field and will serve as a stimulating guide to further research. Audience: This volume will be of interest to researchers and (post)graduate students working in analysis, and in functional analysis in particular. It will also appeal to mathematical engineers, industrial mathematicians, mathematical system theoreticians and mathematical modellers.

Functional Differential Equations

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Author : J. Hale
language : en
Publisher: Springer
Release Date : 1971-05-14

Functional Differential Equations written by J. Hale and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-05-14 with Mathematics categories.

It is hoped that these notes will serve as an introduction to the subject of functional differential equations. The topics are very selective and represent only one particular viewpoint. Complementary material dealing with extensions of closely related topics are given in the notes at the end. A short bibliography is appended as source material for further study. The author is very grateful to the Mathematics Department at UCLA for having extended the invitation to give a series of lectures on functional differ ential equations during the Applied Mathematics Year, 1968-1969. The extreme interest and sincere criticism of the members of the audience were a constant source of inspiration in the preparation of the lectures as well as the notes. Except for Sections 6, 32, 33, 34 and some other minor modifications, the notes represent the material covered in two quarters at UCLA. The author wishes to thank Katherine McDougall and Sandra Spinacci for their excellent preparation of the text. The author is also indebted to Eleanor Addison for her work on the drawings and to Dr. H. T. Banks for his careful proofreading of this material. Jack K. Hale Providence March 4, 1971 v TABLE OF CONTENTS 1. INTRODUCTION •••••.•..••.•••••••••.•••..•.••••••.••••••.••.••.•••.••• 1 2 • A GENERAL INITIAL VALUE PROBLEM 11 3 • EXISTENCE 13 4. CONTINUATION OF SOLUTIONS 16 CONTINUOUS DEPENDENCE AND UNIQUENESS 21 5.

Introduction To Functional Differential Equations

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