Difference equations in normed spaces stability and oscillations / [electronic resource] :

• 作者： Gil
• 其他作者：
  • ScienceDirect (Online service)
• 出版： Amsterdam ;Boston : Elsevier
• 版本：1st ed.
• 叢書名： North-Holland mathematics studies206
• 主題： Difference equations , Normed linear spaces , Electronic books.
• ISBN： 9780444527134 、 0444527133
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: Includes bibliographical references (p. 347-358) and index. 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.
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• 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
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