Introduction to Functional Differential Equations

1. Front Matter

   Pages i-x

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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

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

• Invariant
• boundary element method
• differential equation
• equation
• function
• functional
• manifold
• presentation

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

  Jack K. Hale

• Vrije Universiteit Amsterdam, Amsterdam, The Netherlands

  Sjoerd M. Verduyn Lunel