Difference equations in normed spaces : stability and oscillations
著者
書誌事項
Difference equations in normed spaces : stability and oscillations
（North-Holland mathematics studies, 206）
Elsevier, 2007
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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
目次
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 Operators10. Linear Equations with Slowly Varying Coefficients11. Nonlinear Equations with Autonomous Linear Parts12. Nonlinear Equations with Time-Variant Linear Parts13. Higher Order Linear Difference Equations14. Nonlinear Higher Order Difference Equations15. Input-to-State Stability16. Periodic Solutions of Difference Equations and Orbital Stability17. Discrete Volterra Equations in Banach Spaces18. Convolution type Volterra Difference Equations in Euclidean Spaces and their Perturbations19 Stieltjes Differential Equations20 Volterra-Stieltjes Equations21. Difference Equations with Continuous Time22. Steady States of Difference EquationsAppendix ANotesReferencesList of Main SymbolsIndex
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