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Theory of Functional Differential Equations

  • Book
  • © 1977

Overview

Authors:
  1. Jack K. Hale

    1. Division of Applied Mathematics, Brown University, Providence, USA

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Part of the book series: Applied Mathematical Sciences (AMS, volume 3)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Jack K. Hale
    Pages 1-10

  3. Linear differential difference equations

    • Jack K. Hale
    Pages 11-35

  4. Retarded functional differential equations: basic theory

    • Jack K. Hale
    Pages 36-56

  5. Properties of the solution map

    • Jack K. Hale
    Pages 57-75

  6. Autonomous and periodic processes

    • Jack K. Hale
    Pages 76-102

  7. Stability theory

    • Jack K. Hale
    Pages 103-140

  8. General linear systems

    • Jack K. Hale
    Pages 141-164

  9. Linear autonomous equations

    • Jack K. Hale
    Pages 165-190

  10. Linear periodic systems

    • Jack K. Hale
    Pages 191-203

  11. Perturbed linear systems

    • Jack K. Hale
    Pages 204-226

  12. Behavior near equilibrium and periodic orbits for autonomous equations

    • Jack K. Hale
    Pages 227-244

  13. Periodic solutions of autonomous equations

    • Jack K. Hale
    Pages 245-271

  14. Equations of neutral type

    • Jack K. Hale
    Pages 272-319

  15. Global theory

    • Jack K. Hale
    Pages 320-335

  16. Back Matter

    Pages 337-366
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Keywords

About this book

Since the publication of my lecture notes, Functional Differential Equations in the Applied Mathematical Sciences series, many new developments have occurred. As a consequence, it was decided not to make a few corrections and additions for a second edition of those notes, but to present a more compre­ hensive theory. The present work attempts to consolidate those elements of the theory which have stabilized and also to include recent directions of research. The following chapters were not discussed in my original notes. Chapter 1 is an elementary presentation of linear differential difference equations with constant coefficients of retarded and neutral type. Chapter 4 develops the recent theory of dissipative systems. Chapter 9 is a new chapter on perturbed systems. Chapter 11 is a new presentation incorporating recent results on the existence of periodic solutions of autonomous equations. Chapter 12 is devoted entirely to neutral equations. Chapter 13 gives an introduction to the global and generic theory. There is also an appendix on the location of the zeros of characteristic polynomials. The remainder of the material has been completely revised and updated with the most significant changes occurring in Chapter 3 on the properties of solutions, Chapter 5 on stability, and Chapter lOon behavior near a periodic orbit.

Authors and Affiliations

  • Division of Applied Mathematics, Brown University, Providence, USA

    Jack K. Hale

Bibliographic Information

  • Book Title: Theory of Functional Differential Equations

  • Authors: Jack K. Hale

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-1-4612-9892-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1977

  • Softcover ISBN: 978-1-4612-9894-6Published: 11 November 2011

  • eBook ISBN: 978-1-4612-9892-2Published: 06 December 2012

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 2

  • Number of Pages: X, 366

  • Additional Information: The 1st edition was published with the title: Functional differential equations

  • Topics: Analysis

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