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Functional Differential Equations

  • Book
  • © 1971

Overview

Authors:
  1. Jack K. Hale

    1. Division of Applied Mathematics, Brown University, Providence, USA

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Part of the book series: Applied Mathematical Sciences (AMS, volume 3)

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Table of contents (38 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Introduction

    • Jack K. Hale
    Pages 1-10

  3. A General Initial Value Problem

    • Jack K. Hale
    Pages 11-12

  4. Existence

    • Jack K. Hale
    Pages 13-15

  5. Continuation of Solutions

    • Jack K. Hale
    Pages 16-20

  6. Continuous Dependence and Uniqueness

    • Jack K. Hale
    Pages 21-23

  7. Backward Continuation

    • Jack K. Hale
    Pages 24-29

  8. Caratheodory Conditions

    • Jack K. Hale
    Pages 30-31

  9. Remarks on the Map Defined by Solutions

    • Jack K. Hale
    Pages 32-42

  10. Autonomous Systems

    • Jack K. Hale
    Pages 43-46

  11. Definitions of Stability

    • Jack K. Hale
    Pages 47-50

  12. Sufficient Conditions for Stability of General Systems

    • Jack K. Hale
    Pages 51-64

  13. Sufficient Conditions for Instability

    • Jack K. Hale
    Pages 65-68

  14. Stability in Autonomous Systems

    • Jack K. Hale
    Pages 69-71

  15. An Example of Levin and Nohel

    • Jack K. Hale
    Pages 72-77

  16. An Equation of Volterra

    • Jack K. Hale
    Pages 78-79

  17. Nonhomogeneous Linear Systems

    • Jack K. Hale
    Pages 80-87

  18. The “Adjoint” Equation and Representation of Solutions

    • Jack K. Hale
    Pages 88-90

  19. Stability of Perturbed Systems

    • Jack K. Hale
    Pages 91-93

  20. Linear Autonomous Equations. The Semigroup and Infinitesimal Generator

    • Jack K. Hale
    Pages 94-97
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Keywords

About this book

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.

Authors and Affiliations

  • Division of Applied Mathematics, Brown University, Providence, USA

    Jack K. Hale

Bibliographic Information

  • Book Title: Functional Differential Equations

  • Authors: Jack K. Hale

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-1-4615-9968-5

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1971

  • eBook ISBN: 978-1-4615-9968-5Published: 06 December 2012

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: 238

  • Topics: Analysis

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