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Introduction to Functional Differential Equations / Edition 1

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Overview

The present book builds upon the earlier work of J. Hale, "Theory of Functional Differential Equations" published in 1977. The authors have attempted to maintain the spirit of that book and have retained approximately one-third of the material intact. One major change was a completely new presentation of linear systems (Chapter 6-9) for retarded and neutral functional differential equations. The theory of dissipative systems (Chapter 4) and global attractors was thoroughly 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 (Chapters 1,2,3,9,10). Chapter 12 is also entirely new and contains a guide to active topics of research. In the sections on supplementary remarks, the authors have included many references to recent literature, but, of course, not nearly all, because the subject is so extensive.

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Editorial Reviews

Booknews
Builds on an earlier work by J. Hale, Theory of Functional Differential Equations, 1977. Approximately one-third of the material is left intact. A completely new presentation of linear systems for retarded and neutral functional differential equations is given. The theory of dissipative systems and global attractors is completely redone as well as the invariant manifold theory near equilibrium points and periodic orbits. A more complete theory of neutral equations is presented, and a new guide to active topics of research is added. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780387940762
  • Publisher: Springer New York
  • Publication date: 10/14/1993
  • Series: Applied Mathematical Sciences Series , #99
  • Edition description: 1993
  • Edition number: 1
  • Pages: 449
  • Sales rank: 1,428,308
  • Product dimensions: 1.06 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Preface
Introduction 1
1 Linear differential difference equations 11
2 Functional differential equations: Basic theory 38
3 Properties of the solution map 67
4 Autonomous and periodic processes 100
5 Stability theory 130
6 General linear systems 167
7 Linear autonomous equations 193
8 Periodic systems 236
9 Equations of neutral type 255
10 Near equilibrium and periodic orbits 302
11 Periodic solutions of autonomous equations 331
12 Additional topics 364
Appendix: Stability of characteristic equations 414
Bibliography 419
Index 444
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