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  • Textbook
  • © 1993

Introduction to Functional Differential Equations

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

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  • ISBN: 978-1-4612-4342-7
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Table of contents (13 chapters)

  1. Front Matter

    Pages i-x
  2. Introduction

    • Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 1-10
  3. Linear differential difference equations

    • Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 11-37
  4. Functional differential equations: Basic theory

    • Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 38-66
  5. Properties of the solution map

    • Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 67-99
  6. Autonomous and periodic processes

    • Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 100-129
  7. Stability theory

    • Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 130-166
  8. General linear systems

    • Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 167-192
  9. Linear autonomous equations

    • Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 193-235
  10. Periodic systems

    • Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 236-254
  11. Equations of neutral type

    • Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 255-301
  12. Near equilibrium and periodic orbits

    • Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 302-330
  13. Periodic solutions of autonomous equations

    • Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 331-363
  14. Additional topics

    • Jack K. Hale, Sjoerd M. Verduyn Lunel
    Pages 364-413
  15. Back Matter

    Pages 414-449

About this book

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

  • Georgia Institute of Technology, School of Mathematics, Atlanta, USA

    Jack K. Hale

  • Vrije Universiteit Amsterdam, Amsterdam, The Netherlands

    Sjoerd M. Verduyn Lunel

Bibliographic Information

  • Book Title: Introduction to Functional Differential Equations

  • Authors: Jack K. Hale, Sjoerd M. Verduyn Lunel

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-1-4612-4342-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1993

  • Hardcover ISBN: 978-0-387-94076-2

  • Softcover ISBN: 978-1-4612-8741-4

  • eBook ISBN: 978-1-4612-4342-7

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: X, 450

  • Topics: Analysis

Buying options

eBook USD 79.99
Price excludes VAT (USA)
  • ISBN: 978-1-4612-4342-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 99.99
Price excludes VAT (USA)
Hardcover Book USD 139.99
Price excludes VAT (USA)