Advanced Topics in Difference Equations

Overview

This monograph is a collection of the results the authors have obtained on difference equations and inequalities. In the last few years this discipline has gone through such a dramatic development that it is no longer feasible to present an exhaustive survey of all research. However, this state-of-the-art volume offers a representative overview of the authors' recent work, reflecting some of the major advances in the field as well as the diversity of the subject.
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Paperback (Softcover reprint of hardcover 1st ed. 1997)
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Overview

This monograph is a collection of the results the authors have obtained on difference equations and inequalities. In the last few years this discipline has gone through such a dramatic development that it is no longer feasible to present an exhaustive survey of all research. However, this state-of-the-art volume offers a representative overview of the authors' recent work, reflecting some of the major advances in the field as well as the diversity of the subject.
Audience: This book will be of interest to graduate students and researchers in mathematical analysis and its applications, concentrating on finite differences, ordinary and partial differential equations, real functions and numerical analysis.

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Editorial Reviews

From the Publisher
'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)
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Product Details

  • ISBN-13: 9789048148394
  • Publisher: Springer Netherlands
  • Publication date: 12/10/2010
  • Series: Mathematics and Its Applications (closed) Series , #404
  • Edition description: Softcover reprint of hardcover 1st ed. 1997
  • Edition number: 1
  • Pages: 510
  • Product dimensions: 6.14 (w) x 9.21 (h) x 1.05 (d)

Table of Contents

Preface. 1. Periodic Solutions of First Order Linear Equations. 2. Periodic Solutions of Generalized Difference Systems. 3. Periodic Boundary Value Problems: First Order Systems. 4. Periodic Boundary Value Problems: Second Order Systems. 5. Periodic Solutions of Higher Order Partial Difference Equations. 6. Nonlinear Variation of Parameter Methods: One Independent Variable. 7. Nonlinear Variation of Parameter Methods: Several Independent Variables. 8. Convergence to Equilibria. 9. Asymptotic Behavior of Generalized Difference Systems. 10. Stability of Generalized Difference Systems. 11. Oscillation via Lyapunov's Second Method. 12. Oscillation via Difference Inequalities. 13. Oscillation via Summation Averages. 14. Oscillation for Nonlinear Difference Equations. 15. Oscillation for Quasilinear Difference Equations. 16. Oscillations Generated by Deviating Arguments. 17. Positive Monotone Solutions for Nonlinear Difference Equations. 18. Oscillation for nth Order Nonlinear Difference Equations. 19. Comparison Theorems. 20. Oscillation for Second Order Neutral Delay Difference Equations. 21. Oscillation for Second Order Neutral Delay Difference Equations (Contd.). 22. Oscillation for Higher Order Neutral Delay Difference Equations. 23. Oscillation for Partial Difference Equations I. 24. Oscillation for Partial Difference Equations II. 25. Oscillation for Partial Difference Equations III. 26. Oscillation for Partial Difference Equations IV. 27. A Three-Point Boundary Value Problem. 28. A Singular Boundary Value Problem. 29. Eigenvalues of Boundary Value Problems. 30. Two Solutions of a Boundary Value Problem. 31. (n,p) Boundary Value Problems. 32. Boundary Value Problems Arising in Transport Phenomena. 33. Solutions of m-Point Boundary Value Problems. 34. Two-Point Boundary Value Problems for Generalized Difference Systems. 35. Multi-Point Boundary Value Problems for Generalized Difference Systems. 36. Resonant Boundary Value Problems for Generalized Difference Systems. 37. Boundary Value Problems in Abstract Spaces. 38. Linear Square Optimal Control Problem. 39. Symmetries of Difference Systems on Manifolds. 40. Discrete Polar Coordinates. References.

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