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Advanced Topics in Difference Equations

  • Book
  • © 1997

Overview

Authors:
  1. Ravi P. Agarwal

    1. Department of Mathematics, National University of Singapore, Singapore

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    You can also search for this author in PubMed   Google Scholar

  2. Patricia J. Y. Wong

    1. Division of Mathematics, Nanyang Technological University, Singapore

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Mathematics and Its Applications (MAIA, volume 404)

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Table of contents (40 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Periodic Solutions of First Order Linear Equations

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 1-11

  3. Periodic Solutions of Generalized Difference Systems

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 11-26

  4. Periodic Boundary Value Problems: First Order Systems

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 26-33

  5. Periodic Boundary Value Problems: Second Order Systems

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 33-40

  6. Periodic Solutions of Higher Order Partial Difference Equations

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 41-61

  7. Nonlinear Variation of Parameter Methods: One Independent Variable

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 61-74

  8. Nonlinear Variation of Parameter Methods: Several Independent Variables

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 74-84

  9. Convergence to Equilibria

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 84-96

  10. Asymptotic Behavior of Generalized Difference Systems

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 96-105

  11. Stability of Generalized Difference Systems

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 105-112

  12. Oscillation via Lyapunov’s Second Method

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 112-121

  13. Oscillation via Difference Inequalities

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 121-134

  14. Oscillation via Summation Averages

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 134-149

  15. Oscillation for Nonlinear Difference Equations

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 149-166

  16. Oscillation for Quasilinear Difference Equations

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 167-172

  17. Oscillations Generated by Deviating Arguments

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 172-189

  18. Positive Monotone Solutions for Nonlinear Difference Equations

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 189-197

  19. Oscillation for nth Order Nonlinear Difference Equations

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 197-209

  20. Comparison Theorems

    • Ravi P. Agarwal, Patricia J. Y. Wong
    Pages 209-219
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Keywords

About this book

. The theory of difference equations, the methods used in their solutions and their wide applications have advanced beyond their adolescent stage to occupy a central position in Applicable Analysis. In fact, in the last five years, the proliferation of the subject is witnessed by hundreds of research articles and several monographs, two International Conferences and numerous Special Sessions, and a new Journal as well as several special issues of existing journals, all devoted to the theme of Difference Equations. Now even those experts who believe in the universality of differential equations are discovering the sometimes striking divergence between the continuous and the discrete. There is no doubt that the theory of difference equations will continue to play an important role in mathematics as a whole. In 1992, the first author published a monograph on the subject entitled Difference Equations and Inequalities. This book was an in-depth survey of the field up to the year of publication. Since then, the subject has grown to such an extent that it is now quite impossible for a similar survey, even to cover just the results obtained in the last four years, to be written. In the present monograph, we have collected some of the results which we have obtained in the last few years, as well as some yet unpublished ones.

Reviews

`I think this remarkable monograph should be on the bookshelf of veryone having connection with mathematical analysis and its applications, concentrating on difference equations, numerical analysis, ordinary and partial differential equations.'
Acta Sci. Math., 64 (1998)

Authors and Affiliations

  • Department of Mathematics, National University of Singapore, Singapore

    Ravi P. Agarwal

  • Division of Mathematics, Nanyang Technological University, Singapore

    Patricia J. Y. Wong

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