Theory of Causal Differential Equations

  • V. Lakshmikantham
  • S. Leela
  • Zahia Drici
  • F. A. McRae
Book
Part of the Atlantis Studies in Mathematics for Engineering and Science book series (ASMES, volume 5)

Table of contents

  1. Front Matter
    Pages i-xi
  2. V. Lakshmikantham, S. Leela, Zahia Drici, F. A. McRae
    Pages 1-22
  3. V. Lakshmikantham, S. Leela, Zahia Drici, F. A. McRae
    Pages 23-71
  4. V. Lakshmikantham, S. Leela, Zahia Drici, F. A. McRae
    Pages 73-103
  5. V. Lakshmikantham, S. Leela, Zahia Drici, F. A. McRae
    Pages 105-136
  6. V. Lakshmikantham, S. Leela, Zahia Drici, F. A. McRae
    Pages 137-201
  7. Back Matter
    Pages 203-208

About this book

Introduction

The problems of modern society are both complex and inter-disciplinary. Despite the - parent diversity of problems, however, often tools developed in one context are adaptable to an entirely different situation. For example, consider the well known Lyapunov’s second method. This interesting and fruitful technique has gained increasing signi?cance and has given decisive impetus for modern development of stability theory of discrete and dynamic system. It is now recognized that the concept of Lyapunov function and theory of diff- ential inequalities can be utilized to investigate qualitative and quantitative properties of a variety of nonlinear problems. Lyapunov function serves as a vehicle to transform a given complicated system into a simpler comparison system. Therefore, it is enough to study the properties of the simpler system to analyze the properties of the complicated system via an appropriate Lyapunov function and the comparison principle. It is in this perspective, the present monograph is dedicated to the investigation of the theory of causal differential equations or differential equations with causal operators, which are nonanticipative or abstract Volterra operators. As we shall see in the ?rst chapter, causal differential equations include a variety of dynamic systems and consequently, the theory developed for CDEs (Causal Differential Equations) in general, covers the theory of several dynamic systems in a single framework.

Keywords

Area CDE causal differential equations derivative differential equation equation function functional memory online ordinary differential equation set stability stability theory types

Authors and affiliations

  • V. Lakshmikantham
    • 1
    • 2
  • S. Leela
    • 3
    • 2
  • Zahia Drici
    • 4
  • F. A. McRae
    • 5
  1. 1.Department of Mathematical SciencesFlorida Institute of TechnologyMelbourneUSA
  2. 2.G.V.P. Lakshmikantham’s Institute for Advanced StudiesVisakhapatnamIndia
  3. 3.SUNY at GeneseoGeneseoUSA
  4. 4.Illinois Wesleyan UniversityBloomingtonUSA
  5. 5.The Catholic University of AmericaWashingtonUSA

Bibliographic information

  • DOI https://doi.org/10.2991/978-94-91216-25-1
  • Copyright Information Atlantis Press and the authors 2010
  • Publisher Name Atlantis Press
  • eBook Packages Mathematics and Statistics
  • Online ISBN 978-94-91216-25-1
  • Series Print ISSN 1875-7642