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Asymptotic Equivalence Of Differential Equations And Asymptotically Almost Periodic Solutions
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Book Synopsis Almost Periodicity, Chaos, and Asymptotic Equivalence by : Marat Akhmet
Download or read book Almost Periodicity, Chaos, and Asymptotic Equivalence written by Marat Akhmet and published by Springer. This book was released on 2019-06-20 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central subject of this book is Almost Periodic Oscillations, the most common oscillations in applications and the most intricate for mathematical analysis. Prof. Akhmet's lucid and rigorous examination proves these oscillations are a "regular" component of chaotic attractors. The book focuses on almost periodic functions, first of all, as Stable (asymptotically) solutions of differential equations of different types, presumably discontinuous; and, secondly, as non-isolated oscillations in chaotic sets. Finally, the author proves the existence of Almost Periodic Oscillations (asymptotic and bi-asymptotic) by asymptotic equivalence between systems. The book brings readers' attention to contemporary methods for considering oscillations as well as to methods with strong potential for study of chaos in the future. Providing three powerful instruments for mathematical research of oscillations where dynamics are observable and applied, the book is ideal for engineers as well as specialists in electronics, computer sciences, robotics, neural networks, artificial networks, and biology. Distinctively combines results and methods of the theory of differential equations with thorough investigation of chaotic dynamics with almost periodic ingredients; Provides all necessary mathematical basics in their most developed form, negating the need for any additional sources for readers to start work in the area; Presents a unique method of investigation of discontinuous almost periodic solutions in its unified form, employed to differential equations with different types of discontinuity; Develops the equivalence method to its ultimate effective state such that most important theoretical problems and practical applications can be analyzed by the method.
Book Synopsis Selected Topics in Almost Periodicity by : Marko Kostić
Download or read book Selected Topics in Almost Periodicity written by Marko Kostić and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-11-22 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers uniformly recurrent solutions and c-almost periodic solutions of abstract Volterra integro-differential equations as well as various generalizations of almost periodic functions in Lebesgue spaces with variable coefficients. Treats multi-dimensional almost periodic type functions and their generalizations in adequate detail.
Book Synopsis ALMOST PERIODICITY, CHAOS, AND ASYMPTOTIC EQUIVALENCE. by : MARAT. AKHMET
Download or read book ALMOST PERIODICITY, CHAOS, AND ASYMPTOTIC EQUIVALENCE. written by MARAT. AKHMET and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Almost Periodic Solutions of Differential Equations in Banach Spaces by : Yoshiyuki Hino
Download or read book Almost Periodic Solutions of Differential Equations in Banach Spaces written by Yoshiyuki Hino and published by CRC Press. This book was released on 2001-10-25 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents recent developments in spectral conditions for the existence of periodic and almost periodic solutions of inhomogenous equations in Banach Spaces. Many of the results represent significant advances in this area. In particular, the authors systematically present a new approach based on the so-called evolution semigroups with an original decomposition technique. The book also extends classical techniques, such as fixed points and stability methods, to abstract functional differential equations with applications to partial functional differential equations. Almost Periodic Solutions of Differential Equations in Banach Spaces will appeal to anyone working in mathematical analysis.
Book Synopsis Theory and Applications of Difference Equations and Discrete Dynamical Systems by : Ziyad AlSharawi
Download or read book Theory and Applications of Difference Equations and Discrete Dynamical Systems written by Ziyad AlSharawi and published by Springer. This book was released on 2014-08-22 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Almost Periodic Type Functions and Ergodicity by : Zhang Chuanyi
Download or read book Almost Periodic Type Functions and Ergodicity written by Zhang Chuanyi and published by Springer Science & Business Media. This book was released on 2003-06-30 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of almost periodic functions was first developed by the Danish mathematician H. Bohr during 1925-1926. Then Bohr's work was substantially extended by S. Bochner, H. Weyl, A. Besicovitch, J. Favard, J. von Neumann, V. V. Stepanov, N. N. Bogolyubov, and oth ers. Generalization of the classical theory of almost periodic functions has been taken in several directions. One direction is the broader study of functions of almost periodic type. Related this is the study of ergodic ity. It shows that the ergodicity plays an important part in the theories of function spectrum, semigroup of bounded linear operators, and dynamical systems. The purpose of this book is to develop a theory of almost pe riodic type functions and ergodicity with applications-in particular, to our interest-in the theory of differential equations, functional differen tial equations and abstract evolution equations. The author selects these topics because there have been many (excellent) books on almost periodic functions and relatively, few books on almost periodic type and ergodicity. The author also wishes to reflect new results in the book during recent years. The book consists of four chapters. In the first chapter, we present a basic theory of four almost periodic type functions. Section 1. 1 is about almost periodic functions. To make the reader easily learn the almost periodicity, we first discuss it in scalar case. After studying a classical theory for this case, we generalize it to finite dimensional vector-valued case, and finally, to Banach-valued (including Hilbert-valued) situation.
Download or read book Research in Progress written by and published by . This book was released on 1967 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Half-Linear Differential Equations by : Ondrej Dosly
Download or read book Half-Linear Differential Equations written by Ondrej Dosly and published by Elsevier. This book was released on 2005-07-06 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a systematic and compact treatment of the qualitative theory of half-lineardifferential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE's with p-Laplacian, half-linear difference equations and various more general nonlinear differential equations.- The first complete treatment of the qualitative theory of half-linear differential equations.- Comparison of linear and half-linear theory.- Systematic approach to half-linear oscillation and asymptotic theory.- Comprehensive bibliography and index.- Useful as a reference book in the topic.
Book Synopsis Impulsive Differential Equations by : N Perestyuk
Download or read book Impulsive Differential Equations written by N Perestyuk and published by World Scientific. This book was released on 1995-08-31 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents:General Description of Impulsive Differential SystemsLinear SystemsStability of SolutionsPeriodic and Almost Periodic Impulsive SystemsIntegral Sets of Impulsive SystemsOptimum Control in Impulsive SystemsAsymptotic Study of Oscillations in Impulsive SystemsA Periodic and Almost Periodic Impulsive SystemsBibliographySubject Index Readership: Researchers in nonlinear science. keywords:Differential Equations with Impulses;Linear Systems;Stability;Periodic and Quasi-Periodic Solutions;Integral Sets;Optimal Control “… lucid … the book … will benefit all who are interested in IDE…” Mathematics Abstracts
Book Synopsis Vector-valued Laplace Transforms and Cauchy Problems by : Wolfgang Arendt
Download or read book Vector-valued Laplace Transforms and Cauchy Problems written by Wolfgang Arendt and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear evolution equations in Banach spaces have seen important developments in the last two decades. This is due to the many different applications in the theory of partial differential equations, probability theory, mathematical physics, and other areas, and also to the development of new techniques. One important technique is given by the Laplace transform. It played an important role in the early development of semigroup theory, as can be seen in the pioneering monograph by Rille and Phillips [HP57]. But many new results and concepts have come from Laplace transform techniques in the last 15 years. In contrast to the classical theory, one particular feature of this method is that functions with values in a Banach space have to be considered. The aim of this book is to present the theory of linear evolution equations in a systematic way by using the methods of vector-valued Laplace transforms. It is simple to describe the basic idea relating these two subjects. Let A be a closed linear operator on a Banach space X. The Cauchy problern defined by A is the initial value problern (t 2 0), (CP) {u'(t) = Au(t) u(O) = x, where x E X is a given initial value. If u is an exponentially bounded, continuous function, then we may consider the Laplace transform 00 u(>. ) = 1 e-). . tu(t) dt of u for large real>. .
Book Synopsis Seminar on Differential Equations and Dynamical Systems by : G. S. Jones
Download or read book Seminar on Differential Equations and Dynamical Systems written by G. S. Jones and published by Springer. This book was released on 2006-11-14 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Functional Differential Equations by : J. Hale
Download or read book Functional Differential Equations written by J. Hale and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is hoped that these notes will serve as an introduction to the subject of functional differential equations. The topics are very selective and represent only one particular viewpoint. Complementary material dealing with extensions of closely related topics are given in the notes at the end. A short bibliography is appended as source material for further study. The author is very grateful to the Mathematics Department at UCLA for having extended the invitation to give a series of lectures on functional differ ential equations during the Applied Mathematics Year, 1968-1969. The extreme interest and sincere criticism of the members of the audience were a constant source of inspiration in the preparation of the lectures as well as the notes. Except for Sections 6, 32, 33, 34 and some other minor modifications, the notes represent the material covered in two quarters at UCLA. The author wishes to thank Katherine McDougall and Sandra Spinacci for their excellent preparation of the text. The author is also indebted to Eleanor Addison for her work on the drawings and to Dr. H. T. Banks for his careful proofreading of this material. Jack K. Hale Providence March 4, 1971 v TABLE OF CONTENTS 1. INTRODUCTION •••••.•..••.•••••••••.•••..•.••••••.••••••.••.••.•••.••• 1 2 • A GENERAL INITIAL VALUE PROBLEM 11 3 • EXISTENCE 13 4. CONTINUATION OF SOLUTIONS 16 CONTINUOUS DEPENDENCE AND UNIQUENESS 21 5.
Book Synopsis Stability and Almost Periodic Solutions in Functional Differential Equations by : Tarō Yoshizawa
Download or read book Stability and Almost Periodic Solutions in Functional Differential Equations written by Tarō Yoshizawa and published by . This book was released on 1978 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations by : Anatoli? Mikha?lovich Samo?lenko
Download or read book Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations written by Anatoli? Mikha?lovich Samo?lenko and published by World Scientific. This book was released on 2011 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations with random perturbations are the mathematical models of real-world processes that cannot be described via deterministic laws, and their evolution depends on the random factors. The modern theory of differential equations with random perturbations is on the edge of two mathematical disciplines: random processes and ordinary differential equations. Consequently, the sources of these methods come both from the theory of random processes and from the classic theory of differential equations. This work focuses on the approach to stochastic equations from the perspective of ordinary differential equations. For this purpose, both asymptotic and qualitative methods which appeared in the classical theory of differential equations and nonlinear mechanics are developed.
Book Synopsis Abstract Volterra Integro-Differential Equations by : Marko Kostic
Download or read book Abstract Volterra Integro-Differential Equations written by Marko Kostic and published by . This book was released on 2019-09-19 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of linear Volterra Integro-differental equations has been developing rapidly in the last three decades. This book provides an easy-to-read, concise introduction to the theory of ill-posed abstract Volterra Integro-differential equations. It is accessible to readers whose backgrounds include functions of one complex variable, integration theory and the basic theory of locally convex spaces. Each chapter is further divided into sections and subsections, and contains plenty of examples and open problems.
Download or read book Mathematical Reviews written by and published by . This book was released on 2000 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Behavior of Dissipative Systems by : Jack K. Hale
Download or read book Asymptotic Behavior of Dissipative Systems written by Jack K. Hale and published by American Mathematical Soc.. This book was released on 2010-01-04 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph reports the advances that have been made in the area by the author and many other mathematicians; it is an important source of ideas for the researchers interested in the subject. --Zentralblatt MATH Although advanced, this book is a very good introduction to the subject, and the reading of the abstract part, which is elegant, is pleasant. ... this monograph will be of valuable interest for those who aim to learn in the very rapidly growing subject of infinite-dimensional dissipative dynamical systems. --Mathematical Reviews This book is directed at researchers in nonlinear ordinary and partial differential equations and at those who apply these topics to other fields of science. About one third of the book focuses on the existence and properties of the flow on the global attractor for a discrete or continuous dynamical system. The author presents a detailed discussion of abstract properties and examples of asymptotically smooth maps and semigroups. He also covers some of the continuity properties of the global attractor under perturbation, its capacity and Hausdorff dimension, and the stability of the flow on the global attractor under perturbation. The remainder of the book deals with particular equations occurring in applications and especially emphasizes delay equations, reaction-diffusion equations, and the damped wave equations. In each of the examples presented, the author shows how to verify the existence of a global attractor, and, for several examples, he discusses some properties of the flow on the global attractor.
