Introduction to Functional Differential Equations

  • Jack K. Hale
  • Sjoerd M. Verduyn Lunel

Part of the Applied Mathematical Sciences book series (AMS, volume 99)

Table of contents

  1. Front Matter
    Pages i-x
  2. Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 1-10
  3. Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 11-37
  4. Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 38-66
  5. Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 67-99
  6. Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 100-129
  7. Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 130-166
  8. Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 167-192
  9. Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 193-235
  10. Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 236-254
  11. Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 255-301
  12. Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 302-330
  13. Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 331-363
  14. Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 364-413
  15. Back Matter
    Pages 414-449

About this book

Introduction

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 . . . . . . . . . . . .

Keywords

Invariant boundary element method differential equation equation function functional manifold presentation

Authors and affiliations

  • Jack K. Hale
    • 1
  • Sjoerd M. Verduyn Lunel
    • 2
  1. 1.Georgia Institute of TechnologySchool of MathematicsAtlantaUSA
  2. 2.Vrije Universiteit AmsterdamAmsterdamThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4342-7
  • Copyright Information Springer-Verlag New York 1993
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8741-4
  • Online ISBN 978-1-4612-4342-7
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • About this book
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