# Download Ebook Free Difference Equations In Normed Spaces

## Difference Equations in Normed Spaces

Publisher : Elsevier

Release Date : 2007-01-08

Category : Mathematics

Total pages :378

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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

## Regularity of Difference Equations on Banach Spaces

Publisher : Springer

Release Date : 2014-06-13

Category : Mathematics

Total pages :208

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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.

## Partial Difference Equations

Publisher : CRC Press

Release Date : 2003-02-06

Category : Mathematics

Total pages :288

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Partial Difference Equations treats this major class of functional relations. Such equations have recursive structures so that the usual concepts of increments are important. This book describes mathematical methods that help in dealing with recurrence relations that govern the behavior of variables such as population size and stock price. It is helpful for anyone who has mastered undergraduate mathematical concepts. It offers a concise introduction to the tools and techniques that have proven successful in obtaining results in partial difference equations.

## New Trends in Differential and Difference Equations and Applications

Publisher : MDPI

Release Date : 2019-10-14

Category : Mathematics

Total pages :198

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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.

## Elements of Mathematical Theory of Evolutionary Equations in Banach Spaces

Publisher : World Scientific

Release Date : 2013-05-03

Category : Mathematics

Total pages :408

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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

## Difference Equations, Discrete Dynamical Systems and Applications

Publisher : Springer

Release Date : 2019-06-29

Category : Mathematics

Total pages :382

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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.

## Well-Posedness of Parabolic Difference Equations

Publisher : Birkhäuser

Release Date : 2012-12-06

Category : Mathematics

Total pages :353

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A well-known and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. Modern computers allow the implementation of highly accurate ones; hence, their construction and investigation for various boundary value problems in mathematical physics is generating much current interest. The present monograph is devoted to the construction of highly accurate difference schemes for parabolic boundary value problems, based on Padé approximations. The investigation is based on a new notion of positivity of difference operators in Banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy. Establishing coercivity inequalities allows one to obtain sharp, that is, two-sided estimates of convergence rates. The proofs are based on results in interpolation theory of linear operators. This monograph will be of value to professional mathematicians as well as advanced students interested in the fields of functional analysis and partial differential equations.

## Oscillation Theory for Difference and Functional Differential Equations

Publisher : Springer

Release Date : 2000-06-30

Category : Mathematics

Total pages :337

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This monograph is devoted to a rapidly developing area of research of the qualitative theory of difference and functional differential equations. In fact, in the last 25 years Oscillation Theory of difference and functional differential equations has attracted many researchers. This has resulted in hundreds of research papers in every major mathematical journal, and several books. In the first chapter of this monograph, we address oscillation of solutions to difference equations of various types. Here we also offer several new fundamental concepts such as oscillation around a point, oscillation around a sequence, regular oscillation, periodic oscillation, point-wise oscillation of several orthogonal polynomials, global oscillation of sequences of real valued functions, oscillation in ordered sets, (!, R, ~)-oscillate, oscillation in linear spaces, oscillation in Archimedean spaces, and oscillation across a family. These concepts are explained through examples and supported by interesting results. In the second chapter we present recent results pertaining to the oscil lation of n-th order functional differential equations with deviating argu ments, and functional differential equations of neutral type. We mainly deal with integral criteria for oscillation. While several results of this chapter were originally formulated for more complicated and/or more general differ ential equations, we discuss here a simplified version to elucidate the main ideas of the oscillation theory of functional differential equations. Further, from a large number of theorems presented in this chapter we have selected the proofs of only those results which we thought would best illustrate the various strategies and ideas involved.

## Norm Estimations for Operator Valued Functions and Their Applications

Publisher : CRC Press

Release Date : 1995-08-16

Category : Mathematics

Total pages :376

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Intended for specialists in functional analysis and stability theory, this work presents a systematic exposition of estimations for norms of operator-valued functions, and applies the estimates to spectrum perturbations of linear operators and stability theory. The author demonstrates his own approach to spectrum perturbations.

## New Trends in Difference Equations

Publisher : CRC Press

Release Date : 2002-02-28

Category : Mathematics

Total pages :320

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This series on the International Conference on Difference Equations and Applications has established a tradition within the mathematical community. It brings together scientists from many different areas of research to highlight current interests, challenges and unsolved problems. This volume comprises selected papers presented at the Fifth International Conference on Difference Equations, held at Temuco, Chile. Experts from around the globe examine many facets of difference equations, including extended hyperbolic difference equations, oscillation criteria, invertability, one- and two-dimensional perturbed maps and much more. It provides a valuable source of reference for graduates and researchers.

## Theory and Applications of Difference Equations and Discrete Dynamical Systems

Publisher : Springer

Release Date : 2014-08-22

Category : Mathematics

Total pages :222

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This volume contains the proceedings of the 19th International Conference on Difference Equations and Applications, held at Sultan Qaboos University, Muscat, Oman in May 2013. The conference brought together experts and novices in the theory and applications of difference equations and discrete dynamical systems. The volume features papers in difference equations and discrete time dynamical systems with applications to mathematical sciences and, in particular, mathematical biology, ecology, and epidemiology. It includes four invited papers and eight contributed papers. Topics covered include: competitive exclusion through discrete time models, Benford solutions of linear difference equations, chaos and wild chaos in Lorenz-type systems, advances in periodic difference equations, the periodic decomposition problem, dynamic selection systems and replicator equations, and asymptotic equivalence of difference equations in Banach Space. This book will appeal to researchers, scientists, and educators who work in the fields of difference equations, discrete time dynamical systems and their applications.

## Stochastic Differential and Difference Equations

Publisher : Springer Science & Business Media

Release Date : 1997

Category : Mathematics

Total pages :353

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The Conference on Stochastic Differential Equations held at Gyor, Hungary in August of 1996 was organized jointly by Eotvos Lorand University, Budapest and Kossuth Lajos University Debrecen. It was a satellite event to the 4th World Congress of the Bernoulli society, sponsored by several regional and executive committees of the Society. The papers accepted for publication in the volume come from all over the world and cover almost all contemporary research areas in the field of stochastic equations with many applications to the field of control. The coverage of the book focuses mainly on stochastic partial differential equations and related random fields and on discrete and continuous time parameter ARMA processes and, as well as stochastic differential equations in general. Research workers in stochastics and control theory will find a wide variety of new and fresh ideas expounded in the chapters of this volume. Series: Progress in Systems and Control Theory, Volume 23 Contents: Preface Gyor. The Conference Venue List of Participants Periodically Correlated Solutions to a Class of Stochastic Difference Equations/G.N. Boshnakov On Nonlinear SDE's whose Densities Evolve in a Finite-Dimensional Family/D. Brigo Composition of Skeletons and Support Theorems/M.E. Caballero, B. Fernandez, D. Nualart Invariant Measure for a Wave Equation on a Riemannian Manifold/A.B.Cruzeiro and Z. Haba Ergodic Distributed Control for Parameter Dependent Stochastic Semilinear Systems/T. E. Duncan, B. Maslowski, and B. Pasik-Duncan Dirichlet Forms, Caccioppoli Sets and the Skorohod Equation/M. Fukushima Rate of Convergence of Moments of Spall's SPSA Method/L. Gerencser General Setting for Stochastic Processes Associated with Quantum Fields/S. Albeverio, R. Gielerak, F. Russo On a Class of Semilinear Stochastic Partial Differential Equations/I. Gyongy Parallel Numerical Solution of a Class of Volterra Integro-Differential Equations/G. Heber, C. Lindemann On the Laws of the Oseledets Spaces of Linear Stochastic Differential Equations/P. Imkeller On Stationarity of Additive Bilinear State-space Representation of Time Series/M. Ispany On Convergence of Approximations of Ito-Volterra Equations/A. Kolodii Non-isotropic Ornstein-Uhlenbeck Process and White Noise Analysis/I. Kubo Stochastic Processes with Independent Increments on a Lie Group and their Selfsimilar Properties/H. Kunita Optimal Damping of Forced Oscillations Discrete-time Systems by Output Feedback/A. Lindquist and V. A. Yakubovich Forecast of Levy's Brownian Motion as the Observation Domain Undergoes Deformation/L. Markus A Maximal Inequity for the Skorohod Integral/E. Alós and D. Nualart On the Kinematics of Stochastic Mechanics/M. Pavon Stochastic Equations in Formal Mappings/I. Spectorsky On Fisher's Information Matrix of an ARMA Process/A. Klein and P. Spreij Statistical Analysis of Nonlinear and NonGaussian Time Series/T.S. Rao Bilinear Stochastic Systems with Long Range Dependance in Continous Time/E. Iglói and Gy. Terdik On Support Theorems for Stochastic Nonlinear Partial Differential Equations/K. Twardowska Excitation and Performance in Continuous-time Stochastic Adaptive LQ-control/Z.S. Vagó Invariant Measures for Diffusion Processes in Conuclear Spaces/J. Xiong Degree Theory on Wiener Space and an Application to a Class of SPDEs/ A.S. UEstuenel and M. Zakai On the Interacting Measure-Valued Branching Processes/X. -L. Zhao

## Proceedings of the Conference on Differential & Difference Equations and Applications

Publisher : Hindawi Publishing Corporation

Release Date : 2006

Category : Difference equations

Total pages :1237

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## Positive Solutions of Differential, Difference and Integral Equations

Publisher : Springer Science & Business Media

Release Date : 1998-12-31

Category : Mathematics

Total pages :418

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In analysing nonlinear phenomena many mathematical models give rise to problems for which only nonnegative solutions make sense. In the last few years this discipline has grown dramatically. This state-of-the-art volume offers the authors' recent work, reflecting some of the major advances in the field as well as the diversity of the subject. Audience: This volume will be of interest to graduate students and researchers in mathematical analysis and its applications, whose work involves ordinary differential equations, finite differences and integral equations.

## Semilinear Evolution Equations and Their Applications

Publisher : Springer

Release Date : 2018-10-23

Category : Mathematics

Total pages :189

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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.