Overview
- Authors:
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Jack K. Hale
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Georgia Institute of Technology, School of Mathematics, Atlanta, USA
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Sjoerd M. Verduyn Lunel
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Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
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Table of contents (13 chapters)
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- Jack K. Hale, Sjoerd M. Verduyn Lunel
Pages 1-10
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- Jack K. Hale, Sjoerd M. Verduyn Lunel
Pages 11-37
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- Jack K. Hale, Sjoerd M. Verduyn Lunel
Pages 38-66
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- Jack K. Hale, Sjoerd M. Verduyn Lunel
Pages 67-99
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- Jack K. Hale, Sjoerd M. Verduyn Lunel
Pages 100-129
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- Jack K. Hale, Sjoerd M. Verduyn Lunel
Pages 130-166
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- Jack K. Hale, Sjoerd M. Verduyn Lunel
Pages 167-192
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- Jack K. Hale, Sjoerd M. Verduyn Lunel
Pages 193-235
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- Jack K. Hale, Sjoerd M. Verduyn Lunel
Pages 236-254
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- Jack K. Hale, Sjoerd M. Verduyn Lunel
Pages 255-301
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- Jack K. Hale, Sjoerd M. Verduyn Lunel
Pages 302-330
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- Jack K. Hale, Sjoerd M. Verduyn Lunel
Pages 331-363
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- Jack K. Hale, Sjoerd M. Verduyn Lunel
Pages 364-413
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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-constantsformula............................. 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 . . . . . . . . . . . .
Authors and Affiliations
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Georgia Institute of Technology, School of Mathematics, Atlanta, USA
Jack K. Hale
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Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
Sjoerd M. Verduyn Lunel
