skip to content
Difference equations in normed spaces : stability and oscillations Preview this item
ClosePreview this item
Checking...

Difference equations in normed spaces : stability and oscillations

Publisher: Amsterdam ; Boston : Elsevier, 2007.
Series: North-Holland mathematics studies, 206
Edition/Format:   eBook : Document : English : 1st edView all editions and formats
Summary:
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
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
ISBN: 9780444527134 0444527133
OCLC Number: 731739851
Description: 1 online resource (Online-Datei.)
Contents: 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.
Series Title: North-Holland mathematics studies, 206
Responsibility: M.I. Gil'

Abstract:

Many problems for partial difference and integro-difference equations can be written as difference equations in a normed space. This book deals with the topic of linear and nonlinear difference  Read more...

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.

Similar Items

Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/731739851> # Difference equations in normed spaces stability and oscillations
    a schema:Book, schema:CreativeWork, schema:MediaObject ;
   library:oclcnum "731739851" ;
   library:placeOfPublication <http://dbpedia.org/resource/Boston> ; # Boston
   library:placeOfPublication <http://id.loc.gov/vocabulary/countries/ne> ;
   library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/796500867#Place/amsterdam> ; # Amsterdam
   schema:about <http://id.worldcat.org/fast/893419> ; # Difference equations
   schema:about <http://dewey.info/class/515.625/> ;
   schema:about <http://id.worldcat.org/fast/1039141> ; # Normed linear spaces
   schema:bookEdition "1st ed." ;
   schema:bookFormat schema:EBook ;
   schema:datePublished "2007" ;
   schema:description "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." ;
   schema:description "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.-" ;
   schema:description "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.-" ;
   schema:description "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.-" ;
   schema:description "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.-" ;
   schema:description "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." ;
   schema:description "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.-" ;
   schema:exampleOfWork <http://worldcat.org/entity/work/id/796500867> ;
   schema:genre "Electronic books" ;
   schema:inLanguage "en" ;
   schema:isPartOf <http://experiment.worldcat.org/entity/work/data/796500867#Series/> ; #
   schema:isPartOf <http://experiment.worldcat.org/entity/work/data/796500867#Series/north_holland_mathematics_studies> ; # North-Holland mathematics studies
   schema:name "Difference equations in normed spaces stability and oscillations" ;
   schema:productID "731739851" ;
   schema:publication <http://www.worldcat.org/title/-/oclc/731739851#PublicationEvent/amsterdam_boston_elsevier_2007> ;
   schema:publisher <http://experiment.worldcat.org/entity/work/data/796500867#Agent/elsevier> ; # Elsevier
   schema:url <http://www.ub.unibas.ch/index.php?id=1439> ;
   schema:url <http://www.sciencedirect.com/science/publication?issn=03040208&volume=206> ;
   schema:workExample <http://worldcat.org/isbn/9780444527134> ;
   wdrs:describedby <http://www.worldcat.org/title/-/oclc/731739851> ;
    .


Related Entities

<http://dbpedia.org/resource/Boston> # Boston
    a schema:Place ;
   schema:name "Boston" ;
    .

<http://experiment.worldcat.org/entity/work/data/796500867#Series/> #
    a bgn:PublicationSeries ;
   schema:hasPart <http://www.worldcat.org/oclc/731739851> ; # Difference equations in normed spaces stability and oscillations
   schema:name "" ;
    .

<http://experiment.worldcat.org/entity/work/data/796500867#Series/north_holland_mathematics_studies> # North-Holland mathematics studies
    a bgn:PublicationSeries ;
   schema:hasPart <http://www.worldcat.org/oclc/731739851> ; # Difference equations in normed spaces stability and oscillations
   schema:name "North-Holland mathematics studies" ;
    .

<http://id.worldcat.org/fast/1039141> # Normed linear spaces
    a schema:Intangible ;
   schema:name "Normed linear spaces" ;
    .

<http://id.worldcat.org/fast/893419> # Difference equations
    a schema:Intangible ;
   schema:name "Difference equations" ;
    .

<http://worldcat.org/isbn/9780444527134>
    a schema:ProductModel ;
   schema:isbn "0444527133" ;
   schema:isbn "9780444527134" ;
    .

<http://www.ub.unibas.ch/index.php?id=1439>
   rdfs:comment "Uni Basel: Zugriffsinformationen" ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.