Differential Equations

Introduction to Functional Differential Equations

Name: Introduction to Functional Differential Equations
Brand: Springer
SKU: 9780387940762
Price: 12612.00 INR
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ISBN: 9780387940762

INTRO TO FUNCTIONAL DIFFERENTI

Contributor(s): Hale, Jack K. Author , Verduyn Lunel, Sjoerd M. Author Format: Hardback

Hardback · ISBN 9780387940762

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Key Specifications

ISBN	9780387940762
Subtitle	INTRO TO FUNCTIONAL DIFFERENTI
Publisher	Springer
Publication date	October 1993
Language	English
MRP	£99.99 GBP
Page count	464
Item weight	182 g

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

Introduction to Functional Differential Equations

Key Specifications

Hale, Jack K. Author

Verduyn Lunel, Sjoerd M. Author

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