Atlantis Studies in Mathematics for Engineering and Science

THEORY OF CAUSAL DIFFERENTIAL EQUATIONS

Authors: Leela, S., Lakshmikantham, V.

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About this book

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.

Table of contents (5 chapters)

  • Preliminaries

    Lakshmikantham, V. (et al.)

    Pages 1-22

  • Basic Theory

    Lakshmikantham, V. (et al.)

    Pages 23-71

  • Theoretical ApproximationMethods

    Lakshmikantham, V. (et al.)

    Pages 73-103

  • Stability Theory

    Lakshmikantham, V. (et al.)

    Pages 105-136

  • Miscellaneous Topics in Causal Systems

    Lakshmikantham, V. (et al.)

    Pages 137-201

Buy this book

eBook $89.95
price for USA (gross)
  • ISBN 978-94-91216-25-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
THEORY OF CAUSAL DIFFERENTIAL EQUATIONS
Authors
Series Title
Atlantis Studies in Mathematics for Engineering and Science
Series Volume
5
Copyright
2010
Publisher
Atlantis Press
Copyright Holder
Atlantis Press and the authors
eBook ISBN
978-94-91216-25-1
DOI
10.2991/978-94-91216-25-1
Series ISSN
1875-7642
Edition Number
1
Number of Pages
XI, 208
Topics