Difference Equations in Normed Spaces

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

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  • Author : Michael Gil
  • Publisher : Elsevier
  • Pages : 378 pages
  • ISBN : 9780080469355
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKDifference Equations in Normed Spaces

Difference Equations in Normed Spaces

Difference Equations in Normed Spaces
  • Author : Michael Gil
  • Publisher : Elsevier
  • Release : 08 January 2007
GET THIS BOOKDifference Equations in Normed Spaces

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

New Trends in Differential and Difference Equations and Applications

New Trends in Differential and Difference Equations and Applications
  • Author : Feliz Manuel Minhós,João Fialho
  • Publisher : MDPI
  • Release : 14 October 2019
GET THIS BOOKNew Trends in Differential and Difference Equations and Applications

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,

Difference Equations in Normed Spaces

Difference Equations in Normed Spaces
  • Author : Michael Gil
  • Publisher : Elsevier Science
  • Release : 22 March 2007
GET THIS BOOKDifference Equations in Normed Spaces

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

Form Symmetries and Reduction of Order in Difference Equations

Form Symmetries and Reduction of Order in Difference Equations
  • Author : Hassan Sedaghat
  • Publisher : CRC Press
  • Release : 24 May 2011
GET THIS BOOKForm Symmetries and Reduction of Order in Difference Equations

Form Symmetries and Reduction of Order in Difference Equations presents a new approach to the formulation and analysis of difference equations in which the underlying space is typically an algebraic group. In some problems and applications, an additional algebraic or topological structure is assumed in order to define equations and obtain significant results about them. Reflecting the author’s past research experience, the majority of examples involve equations in finite dimensional Euclidean spaces. The book first introduces difference equations on

Advances in Difference Equations and Discrete Dynamical Systems

Advances in Difference Equations and Discrete Dynamical Systems
  • Author : Saber Elaydi,Yoshihiro Hamaya,Hideaki Matsunaga,Christian Pötzsche
  • Publisher : Springer
  • Release : 13 November 2017
GET THIS BOOKAdvances in Difference Equations and Discrete Dynamical Systems

This volume contains the proceedings of the 22nd International Conference on Difference Equations and Applications, held at Osaka Prefecture University, Osaka, Japan, in July 2016. The conference brought together both experts and novices in the theory and applications of difference equations and discrete dynamical systems. The volume features papers in difference equations and discrete dynamical systems with applications to mathematical sciences and, in particular, mathematical biology and economics. This book will appeal to researchers, scientists, and educators who work in the

Geometric Theory of Discrete Nonautonomous Dynamical Systems

Geometric Theory of Discrete Nonautonomous Dynamical Systems
  • Author : Christian Pötzsche
  • Publisher : Springer
  • Release : 24 August 2010
GET THIS BOOKGeometric Theory of Discrete Nonautonomous Dynamical Systems

Nonautonomous dynamical systems provide a mathematical framework for temporally changing phenomena, where the law of evolution varies in time due to seasonal, modulation, controlling or even random effects. Our goal is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes). These dynamical systems are generated by implicit difference equations, which explicitly depend on time. Compactness and dissipativity conditions are provided for such problems in order to

Elements of Mathematical Theory of Evolutionary Equations in Banach Spaces

Elements of Mathematical Theory of Evolutionary Equations in Banach Spaces
  • Author : Anatoly M Samoilenko,Yuri V Teplinsky
  • Publisher : World Scientific
  • Release : 03 May 2013
GET THIS BOOKElements of Mathematical Theory of Evolutionary Equations in Banach Spaces

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

Elements of Mathematical Theory of Evolutionary Equations in Banach Spaces

Elements of Mathematical Theory of Evolutionary Equations in Banach Spaces
  • Author : Anatoly M. Samoilenko,Yuriy V. Teplinsky
  • Publisher : World Scientific
  • Release : 08 December 2021
GET THIS BOOKElements of Mathematical Theory of Evolutionary Equations in Banach Spaces

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

Difference Equations

Difference Equations
  • Author : Ronald E. Mickens
  • Publisher : CRC Press
  • Release : 06 March 2015
GET THIS BOOKDifference Equations

Difference Equations: Theory, Applications and Advanced Topics, Third Edition provides a broad introduction to the mathematics of difference equations and some of their applications. Many worked examples illustrate how to calculate both exact and approximate solutions to special classes of difference equations. Along with adding several advanced to

Multiplicative Inverse Functional Equations

Multiplicative Inverse Functional Equations
  • Author : B. V. Senthil Kumar,Hemen Dutta
  • Publisher : Springer Nature
  • Release : 06 April 2020
GET THIS BOOKMultiplicative Inverse Functional Equations

This book introduces readers to numerous multiplicative inverse functional equations and their stability results in various spaces. This type of functional equation can be of use in solving many physical problems and also has significant relevance in various scientific fields of research and study. In particular, multiplicative inverse functional equations have applications in electric circuit theory, physics, and relations connecting the harmonic mean and arithmetic mean of several values. Providing a wealth of essential insights and new concepts in the

Mathematics Without Boundaries

Mathematics Without Boundaries
  • Author : Panos M. Pardalos,Themistocles M. Rassias
  • Publisher : Springer
  • Release : 16 September 2014
GET THIS BOOKMathematics Without Boundaries

This volume consists of chapters written by eminent scientists and engineers from the international community and present significant advances in several theories, methods and applications of an interdisciplinary research. These contributions focus on both old and recent developments of Global Optimization Theory, Convex Analysis, Calculus of Variations, Discrete Mathematics and Geometry, as well as several applications to a large variety of concrete problems, including applications of computers to the study of smoothness and analyticity of functions, applications to epidemiological diffusion,

Differential and Difference Equations with Applications

Differential and Difference Equations with Applications
  • Author : Sandra Pinelas,John R. Graef,Stefan Hilger,Peter Kloeden,Christos Schinas
  • Publisher : Springer Nature
  • Release : 21 October 2020
GET THIS BOOKDifferential and Difference Equations with Applications

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.

Functional Analysis, Sobolev Spaces and Partial Differential Equations

Functional Analysis, Sobolev Spaces and Partial Differential Equations
  • Author : Haim Brezis
  • Publisher : Springer Science & Business Media
  • Release : 02 November 2010
GET THIS BOOKFunctional Analysis, Sobolev Spaces and Partial Differential Equations

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover

Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces

Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces
  • Author : Behzad Djafari Rouhani
  • Publisher : CRC Press
  • Release : 20 May 2019
GET THIS BOOKNonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces

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.

Recent Advances in Delay Differential and Difference Equations

Recent Advances in Delay Differential and Difference Equations
  • Author : Ferenc Hartung,Mihály Pituk
  • Publisher : Springer
  • Release : 22 August 2014
GET THIS BOOKRecent Advances in Delay Differential and Difference Equations

Delay differential and difference equations serve as models for a range of processes in biology, physics, engineering and control theory. In this volume, the participants of the International Conference on Delay Differential and Difference Equations and Applications, Balatonfüred, Hungary, July 15-19, 2013 present recent research in this quickly-evolving field. The papers relate to the existence, asymptotic and oscillatory properties of the solutions; stability theory; numerical approximations; and applications to real world phenomena using deterministic and stochastic discrete and continuous dynamical