Difference equations in normed spaces [electronic resource] : stability and oscillations / M.I. Gil'.
- 作者： Gil? M. I. (Mikhail Iosifovich)
- 其他作者：
- 其他題名：
- North-Holland mathematics studies ;
- 出版： Amsterdam ;Boston : Elsevier 2007.
- 叢書名： North-Holland mathematics studies ;206
- 主題： Difference equations. , Normed linear spaces. , Electronic books
- 版本：1st ed.
- ISBN： 0444527133 、 9780444527134
- URL：
An electronic book accessible through the World Wide Web; click for information
- 一般註：Electronic reproduction. Amsterdam : Elsevier Science & Technology, 2007.
- 書目註：Includes bibliographical references (p. 347-358) and index.
-
讀者標籤：
- 系統號： 005163808 | 機讀編目格式
館藏資訊
摘要註
Many problems for partial difference and integro-difference equations can be written as difference equations in a normed space. This book is devoted to linear and nonlinear difference equations in a normed space. Our aim in this monograph is to initiate systematic investigations of the global behavior of solutions of difference equations in a normed space. Our primary concern is to study the asymptotic stability of the equilibrium solution. We are also interested in the existence of periodic and positive solutions. There are many books dealing with the theory of ordinary difference equations. However there are no books dealing systematically with difference equations in a normed space. It is our hope that this book will stimulate interest among mathematicians to develop the stability theory of abstract difference equations. Note that even for ordinary difference equations, the problem of stability analysis continues to attract the attention of many specialists despite its long history. It is still one of the most burning problems, because of the absence of its complete solution, but many general results available for ordinary difference equations (for example, stability by linear approximation) may be easily proved for abstract difference equations. The main methodology presented in this publication is based on a combined use of recent norm estimates for operator-valued functions with the following methods and results: a) the freezing method; b) the Liapunov type equation; c) the method of majorants; d) the multiplicative representation of solutions. In addition, we present stability results for abstract Volterra discrete equations. The book consists of 22 chapters and an appendix. In Chapter 1, some definitions and preliminary results are collected. They are systematically used in the next chapters. In, particular, we recall very briefly some basic notions and results of the theory of operators in Banach and ordered spaces. In addition, stability concepts are pr
內容註
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 Notes References List of Main Symbols Index.