Difference Equations in Normed Spaces

Difference Equations in Normed Spaces

Stability and Oscillations

1st Edition - January 8, 2007

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  • Author: Michael Gil
  • eBook ISBN: 9780080469355

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Difference equations appear as natural descriptions of observed evolution phenomena because most measurements of time evolving variables are discrete. They also appear in the applications of discretization methods for differential, integral and integro-differential equations. The application of the theory of difference equations is rapidly increasing to various fields, such as numerical analysis, control theory, finite mathematics, and computer sciences. This book is devoted to linear and nonlinear difference equations in a normed space. The main methodology presented in this book is based on a combined use of recent norm estimates for operator-valued functions with the following methods and results: The freezing method The Liapunov type equation The method of majorants The multiplicative representation of solutions

Key Features

  • Deals systematically with difference equations in normed spaces
  • Considers new classes of equations that could not be studied in the frameworks of ordinary and partial difference equations
  • Develops the freezing method and presents recent results on Volterra discrete equations
  • Contains an approach based on the estimates for norms of operator functions


The book is intended not only for specialists in stability theory, but for everyone interested in various applications who has had at least a first year graduate level course in analysis.

Table of Contents

  • Preface
    1. Definitions and Preliminaries
    2. Classes of Operators
    3. Functions of Finite Matrices
    4. Norm Estimates for Operator Functions
    5. Spectrum Perturbations
    6. Linear Equations with Constant Operators
    7. Liapunov's Type Equations
    8. Bounds for Spectral Radiuses
    9. Linear Equations with Variable Operators
    10. Linear Equations with Slowly Varying Coefficients
    11. Nonlinear Equations with Autonomous Linear Parts
    12. Nonlinear Equations with Time-Variant Linear Parts
    13. Higher Order Linear Difference Equations
    14. Nonlinear Higher Order Difference Equations
    15. Input-to-State Stability
    16. Periodic Solutions of Difference Equations and Orbital Stability
    17. Discrete Volterra Equations in Banach Spaces
    18. Convolution type Volterra Difference Equations in Euclidean Spaces and their Perturbations
    19 Stieltjes Differential Equations
    20 Volterra-Stieltjes Equations
    21. Difference Equations with Continuous Time
    22. Steady States of Difference Equations
    Appendix A
    List of Main Symbols

Product details

  • No. of pages: 378
  • Language: English
  • Copyright: © Elsevier Science 2007
  • Published: January 8, 2007
  • Imprint: Elsevier Science
  • eBook ISBN: 9780080469355

About the Author

Michael Gil

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