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Difference Equations In Normed Spaces

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Regularity of Difference Equations on Banach Spaces

Regularity of Difference Equations on Banach Spaces Book
Author : Ravi P. Agarwal,Claudio Cuevas,Carlos Lizama
Publisher : Springer
Release : 2014-06-13
ISBN : 3319064479
Language : En, Es, Fr & De

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Book Description :

This work introduces readers to the topic of maximal regularity for difference equations. The authors systematically present the method of maximal regularity, outlining basic linear difference equations along with relevant results. They address recent advances in the field, as well as basic semi group and cosine operator theories in the discrete setting. The authors also identify some open problems that readers may wish to take up for further research. This book is intended for graduate students and researchers in the area of difference equations, particularly those with advance knowledge of and interest in functional analysis.

Difference Equations in Normed Spaces

Difference Equations in Normed Spaces Book
Author : Michael Gil
Publisher : Elsevier
Release : 2007-01-08
ISBN : 9780080469355
Language : En, Es, Fr & De

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Book Description :

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 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

Difference Equations in Normed Spaces

Difference Equations in Normed Spaces Book
Author : Michael Gil
Publisher : Elsevier Science
Release : 2007-03-22
ISBN : 9780444527134
Language : En, Es, Fr & De

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Book Description :

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 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

Asymptotics of Analytic Difference Equations

Asymptotics of Analytic Difference Equations Book
Author : G. K. Immink
Publisher : Springer
Release : 2006-12-08
ISBN : 354039060X
Language : En, Es, Fr & De

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Book Description :

Download Asymptotics of Analytic Difference Equations book written by G. K. Immink, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Elements of Mathematical Theory of Evolutionary Equations in Banach Spaces

Elements of Mathematical Theory of Evolutionary Equations in Banach Spaces Book
Author : Anatoly M Samoilenko,Yuri V Teplinsky
Publisher : World Scientific
Release : 2013-05-03
ISBN : 9814434841
Language : En, Es, Fr & De

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Book Description :

Evolutionary equations are studied in abstract Banach spaces and in spaces of bounded number sequences. For linear and nonlinear difference equations, which are defined on finite-dimensional and infinite-dimensional tori, the problem of reducibility is solved, in particular, in neighborhoods of their invariant sets, and the basics for a theory of invariant tori and bounded semi-invariant manifolds are established. Also considered are the questions on existence and approximate construction of periodic solutions for difference equations in infinite-dimensional spaces and the problem of extendibility of the solutions in degenerate cases. For nonlinear differential equations in spaces of bounded number sequences, new results are obtained in the theory of countable-point boundary-value problems. The book contains new mathematical results that will be useful towards advances in nonlinear mechanics and theoretical physics. Contents:Reducibility Problems for Difference EquationsInvariant Tori of Difference Equations in the Space MPeriodic Solutions of Difference Equations. Extention of SolutionsCountable-Point Boundary-Value Problems for Nonlinear Differential Equations Readership: Graduate students and researchers working in the field of analysis and differential equations. Keywords:Differencial Equations;Difference Equations;Invariant Tori;Bounded Number Sequences;Banach Spaces;Periodic Solutions;ReducibilityKey Features:New theoretical results, complete with proofsTheory developed for equations in infinite-dimensional spacesWritten by leading specialists in the fieldReviews: “The chapters are written so that they are almost independent of each other. The present monograph is helpful to specialists who are concerned with the relevant mathematical problems.” Zentralblatt MATH

New Trends in Differential and Difference Equations and Applications

New Trends in Differential and Difference Equations and Applications Book
Author : Feliz Manuel Minhós,João Fialho
Publisher : MDPI
Release : 2019-10-14
ISBN : 3039215388
Language : En, Es, Fr & De

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Book Description :

This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The objective is to provide an overview of techniques used in these different areas and to emphasize their applicability to real-life phenomena, by the inclusion of examples. These examples not only clarify the theoretical results presented, but also provide insight on how to apply, for future works, the techniques used.

Conditions for Exponential Stability of Difference Equations in Banach Spaces

Conditions for Exponential Stability of Difference Equations in Banach Spaces Book
Author : Mihail Megan,Petre Preda
Publisher : Unknown
Release : 1988
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Conditions for Exponential Stability of Difference Equations in Banach Spaces book written by Mihail Megan,Petre Preda, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces

Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces Book
Author : Behzad Djafari Rouhani
Publisher : CRC Press
Release : 2019-03-15
ISBN : 0429528884
Language : En, Es, Fr & De

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Book Description :

This book is devoted to the study of non-linear evolution and difference equations of first or second order governed by maximal monotone operator. This class of abstract evolution equations contains ordinary differential equations, as well as the unification of some important partial differential equations including heat equation, wave equation, Schrodinger equation, etc. The book contains a collection of the authors' work and applications in this field, as well as those of other authors.

Limit Theorems for Solutions of Stochastic Difference Equations in Banach Spaces with Applications

Limit Theorems for Solutions of Stochastic Difference Equations in Banach Spaces with Applications Book
Author : Valerij A. Kovalʹ,Rainer Schwabe
Publisher : Unknown
Release : 1997
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Limit Theorems for Solutions of Stochastic Difference Equations in Banach Spaces with Applications book written by Valerij A. Kovalʹ,Rainer Schwabe, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Numerical Analysis of Partial Differential Equations

Numerical Analysis of Partial Differential Equations Book
Author : Jacques Louis Lions
Publisher : Springer Science & Business Media
Release : 2011-06-07
ISBN : 9783642110573
Language : En, Es, Fr & De

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Book Description :

S. Albertoni: Alcuni metodi di calcolo nella teoria della diffusione dei neutroni.- I. Babuska: Optimization and numerical stability in computations.- J.H. Bramble: Error estimates in elliptic boundary value problems.- G. Capriz: The numerical approach to hydrodynamic problems.- A. Dou: Energy inequalities in an elastic cylinder.- T. Doupont: On the existence of an iterative method for the solution of elliptic difference equation with an improved work estimate.- J. Douglas, J.R. Cannon: The approximation of harmonic and parabolic functions of half-spaces from interior data.- B.E. Hubbard: Error estimates in the fixed Membrane problem.- K. Jorgens: Calculation of the spectrum of a Schrödinger operator.- A. Lasota: Contingent equations and boundary value problems.- J.L. Lions: Réduction à des problèmes du type Cauchy-Kowalewska.- J.L. Lions: Problèmes aux limites non homogènes à données irrégulières; une méthode d’approximation.- J.L. Lions: Remarques sur l’approximation régularisée de problèmes aux limites.- W.V. Petryshyn: On the approximation-solvability of nonlinear functional equations in normed linear spaces.- P.A. Raviart: Approximation des équations d’évolution par des méthodes variationnelles.- M. Sibony, H. Brezis: Méthodes d’approximation et d’itération pour les operateurs monotones.- V. Thomee: Some topics in stability theory for partial difference operators.

Proceedings of the First International Conference on Difference Equations

Proceedings of the First International Conference on Difference Equations Book
Author : John R. Graef,Saber Elaydi,G. Ladas
Publisher : CRC Press
Release : 1995-12-01
ISBN : 9782884491457
Language : En, Es, Fr & De

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Book Description :

This volume presents papers delivered at the First International Conference on Difference Equations (FICDE) held at Trinity University in San Antonio, Texas, USA. During the course of this meeting, 66 papers were presented by participants from across the United States and more than 20 other countries. Topics of papers include chaotic dynamics, mathematical biology, robust control theory, stochastic differential systems, dynamics of satellite and rocket systems, theory of orthogonal polynomials, and epidemiological modelling. Many current expository papers will be of value to students and researchers in the mathematical and physical sciences.

Advances in Differential and Difference Equations with Applications 2020

Advances in Differential and Difference Equations with Applications 2020 Book
Author : Dumitru Baleanu
Publisher : MDPI
Release : 2021-01-20
ISBN : 3039368702
Language : En, Es, Fr & De

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Book Description :

It is very well known that differential equations are related with the rise of physical science in the last several decades and they are used successfully for models of real-world problems in a variety of fields from several disciplines. Additionally, difference equations represent the discrete analogues of differential equations. These types of equations started to be used intensively during the last several years for their multiple applications, particularly in complex chaotic behavior. A certain class of differential and related difference equations is represented by their respective fractional forms, which have been utilized to better describe non-local phenomena appearing in all branches of science and engineering. The purpose of this book is to present some common results given by mathematicians together with physicists, engineers, as well as other scientists, for whom differential and difference equations are valuable research tools. The reported results can be used by researchers and academics working in both pure and applied differential equations.

Regularity of Difference Equations on Banach Spaces

Regularity of Difference Equations on Banach Spaces Book
Author : Ravi Agarwal,Claudio Cuevas,Carlos Lizama
Publisher : Unknown
Release : 2014-07-31
ISBN : 9783319064482
Language : En, Es, Fr & De

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Book Description :

Download Regularity of Difference Equations on Banach Spaces book written by Ravi Agarwal,Claudio Cuevas,Carlos Lizama, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Differential and Difference Equations with Applications

Differential and Difference Equations with Applications Book
Author : Sandra Pinelas,John R. Graef,Stefan Hilger,Peter Kloeden,Christos Schinas
Publisher : Springer Nature
Release : 2020-10-21
ISBN : 3030563235
Language : En, Es, Fr & De

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Book Description :

This edited volume gathers selected, peer-reviewed contributions presented at the fourth International Conference on Differential & Difference Equations Applications (ICDDEA), which was held in Lisbon, Portugal, in July 2019. First organized in 2011, the ICDDEA conferences bring together mathematicians from various countries in order to promote cooperation in the field, with a particular focus on applications. The book includes studies on boundary value problems; Markov models; time scales; non-linear difference equations; multi-scale modeling; and myriad applications.

New Developments in Difference Equations and Applications

New Developments in Difference Equations and Applications Book
Author : SuiSun Cheng
Publisher : Routledge
Release : 2017-09-29
ISBN : 1351428802
Language : En, Es, Fr & De

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Book Description :

The late Professor Ming-Po Chen was instrumental in making the Third International Conference on Difference Equations a great success. Dedicated to his memory, these proceedings feature papers presented by many of the most prominent mathematicians in the field. It is a comprehensive collection of the latest developments in topics including stability theory, combinatorics, asymptotics, partial difference equations, as well as applications to biological, social, and natural sciences. This volume is an indispensable reference for academic and applied mathematicians, theoretical physicists, systems engineers, and computer and information scientists.

Difference Equations Discrete Dynamical Systems and Applications

Difference Equations  Discrete Dynamical Systems and Applications Book
Author : Saber Elaydi,Christian Pötzsche,Adina Luminiţa Sasu
Publisher : Springer
Release : 2019-06-29
ISBN : 3030200167
Language : En, Es, Fr & De

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Book Description :

The book presents the proceedings of the 23rd International Conference on Difference Equations and Applications, ICDEA 2017, held at the West University of Timișoara, Romania, under the auspices of the International Society of Difference Equations (ISDE), July 24 - 28, 2017. It includes new and significant contributions in the field of difference equations, discrete dynamical systems and their applications in various sciences. Disseminating recent studies and related results and promoting advances, the book appeals to PhD students, researchers, educators and practitioners in the field.

Semilinear Evolution Equations and Their Applications

Semilinear Evolution Equations and Their Applications Book
Author : Toka Diagana
Publisher : Springer
Release : 2018-10-23
ISBN : 303000449X
Language : En, Es, Fr & De

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Book Description :

This book, which is a continuation of Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, presents recent trends and developments upon fractional, first, and second order semilinear difference and differential equations, including degenerate ones. Various stability, uniqueness, and existence results are established using various tools from nonlinear functional analysis and operator theory (such as semigroup methods). Various applications to partial differential equations and the dynamic of populations are amply discussed. This self-contained volume is primarily intended for advanced undergraduate and graduate students, post-graduates and researchers, but may also be of interest to non-mathematicians such as physicists and theoretically oriented engineers. It can also be used as a graduate text on evolution equations and difference equations and their applications to partial differential equations and practical problems arising in population dynamics. For completeness, detailed preliminary background on Banach and Hilbert spaces, operator theory, semigroups of operators, and almost periodic functions and their spectral theory are included as well.

Differential and Difference Equations with Applications

Differential and Difference Equations with Applications Book
Author : Sandra Pinelas,Zuzana Došlá,Ondřej Došlý,Peter E. Kloeden
Publisher : Springer
Release : 2016-09-02
ISBN : 3319328573
Language : En, Es, Fr & De

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Book Description :

Aimed at the community of mathematicians working on ordinary and partial differential equations, difference equations, and functional equations, this book contains selected papers based on the presentations at the International Conference on Differential & Difference Equations and Applications (ICDDEA) 2015, dedicated to the memory of Professor Georg Sell. Contributions include new trends in the field of differential and difference equations, applications of differential and difference equations, as well as high-level survey results. The main aim of this recurring conference series is to promote, encourage, cooperate, and bring together researchers in the fields of differential & difference equations. All areas of differential and difference equations are represented, with special emphasis on applications.

Advances in Difference Equations

Advances in Difference Equations Book
Author : Saber N. Elaydi,I. Gyori,G. Ladas
Publisher : CRC Press
Release : 1998-01-29
ISBN : 9789056995218
Language : En, Es, Fr & De

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Book Description :

The recent surge in research activity in difference equations and applications has been driven by the wide applicability of discrete models to such diverse fields as biology, engineering, physics, economics, chemistry, and psychology. The 68 papers that make up this book were presented by an international group of experts at the Second International Conference on Difference Equations, held in Veszprém, Hungary, in August, 1995. Featuring contributions on such topics as orthogonal polynomials, control theory, asymptotic behavior of solutions, stability theory, special functions, numerical analysis, oscillation theory, models of vibrating string, models of chemical reactions, discrete competition systems, the Liouville-Green (WKB) method, and chaotic phenomena, this volume offers a comprehensive review of the state of the art in this exciting field.

Asymptotic Integration of Differential and Difference Equations

Asymptotic Integration of Differential and Difference Equations Book
Author : Sigrun Bodine,Donald A. Lutz
Publisher : Springer
Release : 2015-05-26
ISBN : 331918248X
Language : En, Es, Fr & De

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Book Description :

This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers in asymptotic integration as well to non-experts who are interested in the asymptotic analysis of linear differential and difference equations. It will additionally be of interest to students in mathematics, applied sciences, and engineering. Linear algebra and some basic concepts from advanced calculus are prerequisites.