Applied Mathematical Sciences

Introduction to Functional Differential Equations

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

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About this Textbook

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

Table of contents (13 chapters)

  • Introduction

    Hale, Jack K. (et al.)

    Pages 1-10

  • Linear differential difference equations

    Hale, Jack K. (et al.)

    Pages 11-37

  • Functional differential equations: Basic theory

    Hale, Jack K. (et al.)

    Pages 38-66

  • Properties of the solution map

    Hale, Jack K. (et al.)

    Pages 67-99

  • Autonomous and periodic processes

    Hale, Jack K. (et al.)

    Pages 100-129

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-1-4612-4342-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.00
price for USA
  • ISBN 978-0-387-94076-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA
  • ISBN 978-1-4612-8741-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Functional Differential Equations
Authors
Series Title
Applied Mathematical Sciences
Series Volume
99
Copyright
1993
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-4342-7
DOI
10.1007/978-1-4612-4342-7
Hardcover ISBN
978-0-387-94076-2
Softcover ISBN
978-1-4612-8741-4
Series ISSN
0066-5452
Edition Number
1
Number of Pages
X, 450
Topics