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Theory of Differential Equations with Unbounded Delay

  • V. Lakshmikantham
  • Lizhi Wen
  • Binggen Zhang

Part of the Mathematics and Its Applications book series (MAIA, volume 298)

Table of contents

  1. Front Matter
    Pages i-xi
  2. V. Lakshmikantham, Lizhi Wen, Binggen Zhang
    Pages 1-14
  3. V. Lakshmikantham, Lizhi Wen, Binggen Zhang
    Pages 15-45
  4. V. Lakshmikantham, Lizhi Wen, Binggen Zhang
    Pages 47-73
  5. V. Lakshmikantham, Lizhi Wen, Binggen Zhang
    Pages 75-126
  6. V. Lakshmikantham, Lizhi Wen, Binggen Zhang
    Pages 127-175
  7. V. Lakshmikantham, Lizhi Wen, Binggen Zhang
    Pages 177-244
  8. V. Lakshmikantham, Lizhi Wen, Binggen Zhang
    Pages 245-273
  9. V. Lakshmikantham, Lizhi Wen, Binggen Zhang
    Pages 275-305
  10. V. Lakshmikantham, Lizhi Wen, Binggen Zhang
    Pages 307-354
  11. Back Matter
    Pages 355-385

About this book

Introduction

Because the theory of equations with delay terms occurs in a variety of contexts, it is important to provide a framework, whenever possible, to handle as many cases as possible simultaneously so as to bring out a better insight and understanding of the subtle differences of the various equations with delays. Furthermore, such a unified theory would avoid duplication and expose open questions that are significant for future research.
It is in this spirit that the authors view the importance of their monograph, which presents a systematic and unified theory of recent developments of equations with unbounded delay, describes the current state of the theory showing the essential unity achieved, and provides a general structure applicable to a variety of problems.
It is the first book that:
(i) presents a unified framework to investigate the basic existence theory for a variety of equations with delay;
(ii) treats the classification of equations with memory precisely so as to bring out the subtle differences between them;
(iii) develops a systematic study of stability theory in terms of two different measures which includes several known concepts; and
(iv) exhibits the advantages of employing Lyapunov functions on product spaces as well as the method of perturbing Lyapunov functions.
This book will be of value to researchers and advanced graduate students in mathematics, electrical engineering and biomathematics.

Keywords

DEX Finite behavior development differential equation eXist electrical engineering equation framework function functions mathematics memory stability stability theory

Authors and affiliations

  • V. Lakshmikantham
    • 1
  • Lizhi Wen
    • 2
  • Binggen Zhang
    • 3
  1. 1.Department of Applied MathematicsFlorida Institute of TechnologyMelbourneUSA
  2. 2.Department of MathematicsSouth China Normal UniversityGuangzhouPeople’s Republic of China
  3. 3.Department of Applied MathematicsOcean University of QingdaoQingdaoPeople’s Republic of China

Bibliographic information