Difference equations in normed spaces (Record no. 21836)
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| control field | ocn162131418 |
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| control field | OCoLC |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20141103172225.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
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| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
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| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 070802s2007 ne ob 001 0 eng d |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | |
| Language of cataloging | eng |
| Transcribing agency | OPELS |
| Modifying agency | OCLCG |
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| 019 ## - | |
| -- | 85863138 |
| -- | 648133074 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780444527134 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 0444527133 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780080469355 (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 0080469353 (electronic bk.) |
| 029 1# - (OCLC) | |
| OCLC library identifier | NZ1 |
| System control number | 11778291 |
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| OCLC library identifier | AU@ |
| System control number | 000048131115 |
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| OCLC library identifier | DEBBG |
| System control number | BV039834065 |
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| OCLC library identifier | NZ1 |
| System control number | 14540074 |
| 029 1# - (OCLC) | |
| OCLC library identifier | AU@ |
| System control number | 000051561507 |
| 029 1# - (OCLC) | |
| OCLC library identifier | NZ1 |
| System control number | 15177281 |
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| OCLC library identifier | DEBBG |
| System control number | BV036962184 |
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| OCLC library identifier | AU@ |
| System control number | 000053283251 |
| 029 1# - (OCLC) | |
| OCLC library identifier | NLGGC |
| System control number | 380800799 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)162131418 |
| Canceled/invalid control number | (OCoLC)85863138 |
| -- | (OCoLC)648133074 |
| 037 ## - SOURCE OF ACQUISITION | |
| Stock number | 132894:133017 |
| Source of stock number/acquisition | Elsevier Science & Technology |
| Note | http://www.sciencedirect.com |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA431 |
| Item number | .G5868 2007eb |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 005000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 034000 |
| Source | bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515/.625 |
| Edition number | 22 |
| 049 ## - LOCAL HOLDINGS (OCLC) | |
| Holding library | TEFA |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Gil�, M. I. |
| Fuller form of name | (Mikhail Iosifovich) |
| 245 10 - TITLE STATEMENT | |
| Title | Difference equations in normed spaces |
| Medium | [electronic resource] : |
| Remainder of title | stability and oscillations / |
| Statement of responsibility, etc. | M.I. Gil'. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc. | Amsterdam ; |
| -- | Boston : |
| Name of publisher, distributor, etc. | Elsevier, |
| Date of publication, distribution, etc. | 2007. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (xvi, 362 p.) |
| 490 1# - SERIES STATEMENT | |
| Series statement | North-Holland mathematics studies ; |
| Volume/sequential designation | 206 |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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 presented and Liapunov's functions are introduced. In Chapter 2 we review various classes of linear operators and their spectral properties. As examples, infinite matrices are considered. In Chapters 3 and 4, estimates for the norms of operator-valued and matrix-valued functions are suggested. In particular, we consider Hilbert-Schmidt, Neumann-Schatten, quasi-Hermitian and quasiunitary operators. These classes contain numerous infinite matrices arising in applications. In Chapter 5, some perturbation results for linear operators in a Hilbert space are presented. These results are then used in the next chapters to derive bounds for the spectral radiuses. Chapters 6-14 are devoted to asymptotic and exponential stabilities, as well as boundedness of solutions of linear and nonlinear difference equations. In Chapter 6 we investigate the linear equation with a bounded constant operator acting in a Banach space. Chapter 7 is concerned with the Liapunov type operator equation. Chapter 8 deals with estimates for the spectral radiuses of concrete operators, in particular, for infinite matrices. These bounds enable the formulation of explicit stability conditions. In Chapters 9 and 10 we consider nonautonomous (time-variant) linear equations. An essential role in this chapter is played by the evolution operator. In addition, we use the "freezing" method and multiplicative representations of solutions to construct the majorants for linear equations. Chapters 11 and 12 are devoted to semilinear autonomous and nonautonomous equations. Chapters 13 and 14 are concerned with linear and nonlinear higher order difference equations. Chapter 15 is devoted to the input-to-state stability. In Chapter 16 we study periodic solutions of linear and nonlinear difference equations in a Banach space, as well as the global orbital stability of solutions of vector difference equations. Chapters 17 and 18 deal with linear and nonlinear Volterra discrete equations in a Banach space. An important role in these chapter is played by operator pencils. Chapter 19 deals with a class of the Stieltjes differential equations. These equations generalize difference and differential equations. We apply estimates for norms of operator valued functions and properties of the multiplicative integral to certain classes of linear and nonlinear Stieltjes differential equations to obtain solution estimates that allow us to study the stability and boundedness of solutions. We also show the existence and uniqueness of solutions as well as the continuous dependence of the solutions on the time integrator. Chapter 20 provides some results regarding the Volterra--Stieltjes equations. The Volterra--Stieltjes equations include Volterra difference and Volterra integral equations. We obtain estimates for the norms of solutions of the Volterra--Stieltjes equation. Chapter 21 is devoted to difference equations with continuous time. In Chapter 22, we suggest some conditions for the existence of nontrivial and positive steady states of difference equations, as well as bounds for the stationary solutions. - Deals systematically with difference equations in normed spaces - Considers new classes of equations that could not be studied in the frameworks of ordinary and partial difference equations - Develops the freezing method and presents recent results on Volterra discrete equations - Contains an approach based on the estimates for norms of operator functions. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc | Includes bibliographical references (p. 347-358) and index. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on print version record. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Difference equations. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Normed linear spaces. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | MATHEMATICS |
| General subdivision | Calculus. |
| Source of heading or term | bisacsh |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | MATHEMATICS |
| General subdivision | Mathematical Analysis. |
| Source of heading or term | bisacsh |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Difference equations. |
| Source of heading or term | fast |
| Authority record control number | (OCoLC)fst00893419 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Normed linear spaces. |
| Source of heading or term | fast |
| Authority record control number | (OCoLC)fst01039141 |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Gil�, M.I. (Mikhail Iosifovich). |
| Title | Difference equations in normed spaces. |
| Edition | 1st ed. |
| Place, publisher, and date of publication | Amsterdam ; Boston : Elsevier, 2007 |
| International Standard Book Number | 9780444527134 |
| -- | 0444527133 |
| Record control number | (DLC) 2006052164 |
| -- | (OCoLC)74967021 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | North-Holland mathematics studies ; |
| Volume number/sequential designation | 206. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Materials specified | ScienceDirect |
| Uniform Resource Identifier | <a href="http://www.sciencedirect.com/science/book/9780444527134">http://www.sciencedirect.com/science/book/9780444527134</a> |
| 856 4# - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="http://www.sciencedirect.com/science/publication?issn=03040208&volume=206">http://www.sciencedirect.com/science/publication?issn=03040208&volume=206</a> |
| Materials specified | Volltext |
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| -- | 2534725 |
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| -- | ebrary |
| -- | EBRY |
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| -- | EBSCOhost |
| -- | EBSC |
| -- | 186086 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | E(electronic)-Books |
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| -- | TEF |
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