Theory Of Functional Differential Equations

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Theory of Functional Differential Equations

Author : Jack K. Hale
Publisher : Springer Science & Business Media
ISBN 13 : 146129892X
Total Pages : 374 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Theory of Functional Differential Equations by : Jack K. Hale

Download or read book Theory of Functional Differential Equations written by Jack K. Hale and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of my lecture notes, Functional Differential Equations in the Applied Mathematical Sciences series, many new developments have occurred. As a consequence, it was decided not to make a few corrections and additions for a second edition of those notes, but to present a more compre hensive theory. The present work attempts to consolidate those elements of the theory which have stabilized and also to include recent directions of research. The following chapters were not discussed in my original notes. Chapter 1 is an elementary presentation of linear differential difference equations with constant coefficients of retarded and neutral type. Chapter 4 develops the recent theory of dissipative systems. Chapter 9 is a new chapter on perturbed systems. Chapter 11 is a new presentation incorporating recent results on the existence of periodic solutions of autonomous equations. Chapter 12 is devoted entirely to neutral equations. Chapter 13 gives an introduction to the global and generic theory. There is also an appendix on the location of the zeros of characteristic polynomials. The remainder of the material has been completely revised and updated with the most significant changes occurring in Chapter 3 on the properties of solutions, Chapter 5 on stability, and Chapter lOon behavior near a periodic orbit.

Applied Theory of Functional Differential Equations

Author : V. Kolmanovskii
Publisher : Springer Science & Business Media
ISBN 13 : 9401580847
Total Pages : 246 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Applied Theory of Functional Differential Equations by : V. Kolmanovskii

Download or read book Applied Theory of Functional Differential Equations written by V. Kolmanovskii and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an introduction to the properties of functional differential equations and their applications in diverse fields such as immunology, nuclear power generation, heat transfer, signal processing, medicine and economics. In particular, it deals with problems and methods relating to systems having a memory (hereditary systems). The book contains eight chapters. Chapter 1 explains where functional differential equations come from and what sort of problems arise in applications. Chapter 2 gives a broad introduction to the basic principle involved and deals with systems having discrete and distributed delay. Chapters 3-5 are devoted to stability problems for retarded, neutral and stochastic functional differential equations. Problems of optimal control and estimation are considered in Chapters 6-8. For applied mathematicians, engineers, and physicists whose work involves mathematical modeling of hereditary systems. This volume can also be recommended as a supplementary text for graduate students who wish to become better acquainted with the properties and applications of functional differential equations.

Introduction to Functional Differential Equations

Author : Jack K. Hale
Publisher : Springer Science & Business Media
ISBN 13 : 1461243424
Total Pages : 458 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Introduction to Functional Differential Equations by : Jack K. Hale

Download or read book Introduction to Functional Differential Equations written by Jack K. Hale and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book builds upon an earlier work of J. Hale, "Theory of Func tional Differential Equations" published in 1977. We have tried to maintain the spirit of that book and have retained approximately one-third of the material intact. One major change was a complete new presentation of lin ear systems (Chapters 6~9) for retarded and neutral functional differential equations. The theory of dissipative systems (Chapter 4) and global at tractors was completely revamped as well as the invariant manifold theory (Chapter 10) near equilibrium points and periodic orbits. A more complete theory of neutral equations is presented (see Chapters 1, 2, 3, 9, and 10). Chapter 12 is completely new and contains a guide to active topics of re search. In the sections on supplementary remarks, we have included many references to recent literature, but, of course, not nearly all, because the subject is so extensive. Jack K. Hale Sjoerd M. Verduyn Lunel Contents Preface............................................................ v Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . 1. Linear differential difference equations . . . . . . . . . . . . . . 11 . . . . . . 1.1 Differential and difference equations. . . . . . . . . . . . . . . . . . . . 11 . . . . . . . . 1.2 Retarded differential difference equations. . . . . . . . . . . . . . . . 13 . . . . . . . 1.3 Exponential estimates of x( ¢,f) . . . . . . . . . . . . . . . . . . . . . 15 . . . . . . . . . . 1.4 The characteristic equation . . . . . . . . . . . . . . . . . . . . . . . . 17 . . . . . . . . . . . . 1.5 The fundamental solution. . . . . . . . . . . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . 1.6 The variation-of-constants formula............................. 23 1. 7 Neutral differential difference equations . . . . . . . . . . . . . . . . . 25 . . . . . . . 1.8 Supplementary remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . 34 . . . . . . . . . . . . . 2. Functional differential equations: Basic theory . . . . . . . . 38 . . 2.1 Definition of a retarded equation. . . . . . . . . . . . . . . . . . . . . . 38 . . . . . . . . . 2.2 Existence, uniqueness, and continuous dependence . . . . . . . . . . 39 . . . 2.3 Continuation of solutions . . . . . . . . . . . . . . . . . . . . . . . . . . 44 . . . . . . . . . . . .

Nonoscillation Theory of Functional Differential Equations with Applications

Author : Ravi P. Agarwal
Publisher : Springer Science & Business Media
ISBN 13 : 1461434556
Total Pages : 526 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Nonoscillation Theory of Functional Differential Equations with Applications by : Ravi P. Agarwal

Download or read book Nonoscillation Theory of Functional Differential Equations with Applications written by Ravi P. Agarwal and published by Springer Science & Business Media. This book was released on 2012-04-23 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph explores nonoscillation and existence of positive solutions for functional differential equations and describes their applications to maximum principles, boundary value problems and stability of these equations. In view of this objective the volume considers a wide class of equations including, scalar equations and systems of different types, equations with variable types of delays and equations with variable deviations of the argument. Each chapter includes an introduction and preliminaries, thus making it complete. Appendices at the end of the book cover reference material. Nonoscillation Theory of Functional Differential Equations with Applications is addressed to a wide audience of researchers in mathematics and practitioners.

Stability by Fixed Point Theory for Functional Differential Equations

Author : T. A. Burton
Publisher : Courier Corporation
ISBN 13 : 0486153320
Total Pages : 366 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Stability by Fixed Point Theory for Functional Differential Equations by : T. A. Burton

Download or read book Stability by Fixed Point Theory for Functional Differential Equations written by T. A. Burton and published by Courier Corporation. This book was released on 2013-04-16 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first general introduction to stability of ordinary and functional differential equations by means of fixed point techniques, this text is suitable for advanced undergraduates and graduate students. 2006 edition.

Bifurcation Theory of Functional Differential Equations

Author : Shangjiang Guo
Publisher : Springer Science & Business Media
ISBN 13 : 1461469929
Total Pages : 289 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Bifurcation Theory of Functional Differential Equations by : Shangjiang Guo

Download or read book Bifurcation Theory of Functional Differential Equations written by Shangjiang Guo and published by Springer Science & Business Media. This book was released on 2013-07-30 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering and the study of FDEs has been a major source of inspiration for advancement in nonlinear analysis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and frameworks for the investigation of bifurcation phenomena of FDEs depending on parameters with chap. This well illustrated book aims to be self contained so the readers will find in this book all relevant materials in bifurcation, dynamical systems with symmetry, functional differential equations, normal forms and center manifold reduction. This material was used in graduate courses on functional differential equations at Hunan University (China) and York University (Canada).

Theory and Applications of Partial Functional Differential Equations

Author : Jianhong Wu
Publisher : Springer Science & Business Media
ISBN 13 : 1461240506
Total Pages : 441 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Theory and Applications of Partial Functional Differential Equations by : Jianhong Wu

Download or read book Theory and Applications of Partial Functional Differential Equations written by Jianhong Wu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical systems point of view. The required prerequisites for that book are at a level of a graduate student. The style of presentation will be appealing to people trained and interested in qualitative theory of ordinary and functional differential equations.

Oscillation Theory for Difference and Functional Differential Equations

Author : R.P. Agarwal
Publisher : Springer Science & Business Media
ISBN 13 : 9401594015
Total Pages : 344 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Oscillation Theory for Difference and Functional Differential Equations by : R.P. Agarwal

Download or read book Oscillation Theory for Difference and Functional Differential Equations written by R.P. Agarwal and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Functional Differential Equations with Infinite Delay

Author : Yoshiyuki Hino
Publisher : Springer
ISBN 13 : 3540473882
Total Pages : 326 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Functional Differential Equations with Infinite Delay by : Yoshiyuki Hino

Download or read book Functional Differential Equations with Infinite Delay written by Yoshiyuki Hino and published by Springer. This book was released on 2006-11-14 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the theory of functional differential equations with infinite delay, there are several ways to choose the space of initial functions (phase space); and diverse (duplicated) theories arise, according to the choice of phase space. To unify the theories, an axiomatic approach has been taken since the 1960's. This book is intended as a guide for the axiomatic approach to the theory of equations with infinite delay and a culmination of the results obtained in this way. It can also be used as a textbook for a graduate course. The prerequisite knowledge is foundations of analysis including linear algebra and functional analysis. It is hoped that the book will prepare students for further study of this area, and that will serve as a ready reference to the researchers in applied analysis and engineering sciences.

Oscillation Theory for Functional Differential Equations

Author : Lynn Erbe
Publisher : CRC Press
ISBN 13 : 9780824795986
Total Pages : 500 pages
Book Rating : 4.7/5 (959 download)

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Book Synopsis Oscillation Theory for Functional Differential Equations by : Lynn Erbe

Download or read book Oscillation Theory for Functional Differential Equations written by Lynn Erbe and published by CRC Press. This book was released on 1994-12-08 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines developments in the oscillatory and nonoscillatory properties of solutions for functional differential equations, presenting basic oscillation theory as well as recent results. The book shows how to extend the techniques for boundary value problems of ordinary differential equations to those of functional differential equations.

Functional Differential Equations

Author : Constantin Corduneanu
Publisher : John Wiley & Sons
ISBN 13 : 1119189489
Total Pages : 368 pages
Book Rating : 4.1/5 (191 download)

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Book Synopsis Functional Differential Equations by : Constantin Corduneanu

Download or read book Functional Differential Equations written by Constantin Corduneanu and published by John Wiley & Sons. This book was released on 2016-03-25 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features new results and up-to-date advances in modeling and solving differential equations Introducing the various classes of functional differential equations, Functional Differential Equations: Advances and Applications presents the needed tools and topics to study the various classes of functional differential equations and is primarily concerned with the existence, uniqueness, and estimates of solutions to specific problems. The book focuses on the general theory of functional differential equations, provides the requisite mathematical background, and details the qualitative behavior of solutions to functional differential equations. The book addresses problems of stability, particularly for ordinary differential equations in which the theory can provide models for other classes of functional differential equations, and the stability of solutions is useful for the application of results within various fields of science, engineering, and economics. Functional Differential Equations: Advances and Applications also features: • Discussions on the classes of equations that cannot be solved to the highest order derivative, and in turn, addresses existence results and behavior types • Oscillatory motion and solutions that occur in many real-world phenomena as well as in man-made machines • Numerous examples and applications with a specific focus on ordinary differential equations and functional differential equations with finite delay • An appendix that introduces generalized Fourier series and Fourier analysis after periodicity and almost periodicity • An extensive Bibliography with over 550 references that connects the presented concepts to further topical exploration Functional Differential Equations: Advances and Applications is an ideal reference for academics and practitioners in applied mathematics, engineering, economics, and physics. The book is also an appropriate textbook for graduate- and PhD-level courses in applied mathematics, differential and difference equations, differential analysis, and dynamics processes. CONSTANTIN CORDUNEANU, PhD, is Emeritus Professor in the Department of Mathematics at The University of Texas at Arlington, USA. The author of six books and over 200 journal articles, he is currently Associate Editor for seven journals; a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Romanian Academy; and past president of the American Romanian Academy of Arts and Sciences. YIZENG LI, PhD, is Professor in the Department of Mathematics at Tarrant County College, USA. He is a member of the Society for Industrial and Applied Mathematics. MEHRAN MAHDAVI, PhD, is Professor in the Department of Mathematics at Bowie State University, USA. The author of numerous journal articles, he is a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Mathematical Association of America.

Delay and Functional Differential Equations and Their Applications

Author : Klaus Schmitt
Publisher : Elsevier
ISBN 13 : 1483272338
Total Pages : 412 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Delay and Functional Differential Equations and Their Applications by : Klaus Schmitt

Download or read book Delay and Functional Differential Equations and Their Applications written by Klaus Schmitt and published by Elsevier. This book was released on 2014-05-10 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Delay and Functional Differential Equations and Their Applications provides information pertinent to the fundamental aspects of functional differential equations and its applications. This book covers a variety of topics, including qualitative and geometric theory, control theory, Volterra equations, numerical methods, the theory of epidemics, problems in physiology, and other areas of applications. Organized into two parts encompassing 25 chapters, this book begins with an overview of problems involving functional differential equations with terminal conditions in function spaces. This text then examines the numerical methods for functional differential equations. Other chapters consider the theory of radiative transfer, which give rise to several interesting functional partial differential equations. This book discusses as well the theory of embedding fields, which studies systems of nonlinear functional differential equations that can be derived from psychological postulates and interpreted as neural networks. The final chapter deals with the usefulness of the flip-flop circuit. This book is a valuable resource for mathematicians.

Nonoscillation and Oscillation Theory for Functional Differential Equations

Author : Ravi P. Agarwal
Publisher : CRC Press
ISBN 13 : 0203025741
Total Pages : 400 pages
Book Rating : 4.2/5 (3 download)

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Book Synopsis Nonoscillation and Oscillation Theory for Functional Differential Equations by : Ravi P. Agarwal

Download or read book Nonoscillation and Oscillation Theory for Functional Differential Equations written by Ravi P. Agarwal and published by CRC Press. This book was released on 2004-08-30 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book summarizes the qualitative theory of differential equations with or without delays, collecting recent oscillation studies important to applications and further developments in mathematics, physics, engineering, and biology. The authors address oscillatory and nonoscillatory properties of first-order delay and neutral delay differential eq

Oscillation Theory for Neutral Differential Equations with Delay

Author : D.D Bainov
Publisher : CRC Press
ISBN 13 : 9780750301428
Total Pages : 296 pages
Book Rating : 4.3/5 (14 download)

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Book Synopsis Oscillation Theory for Neutral Differential Equations with Delay by : D.D Bainov

Download or read book Oscillation Theory for Neutral Differential Equations with Delay written by D.D Bainov and published by CRC Press. This book was released on 1991-01-01 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: With neutral differential equations, any lack of smoothness in initial conditions is not damped and so they have proven to be difficult to solve. Until now, there has been little information to help with this problem. Oscillation Theory for Neutral Differential Equations with Delay fills a vacuum in qualitative theory of functional differential equations of neutral type. With much of the presented material previously unavailable outside Eastern Europe, this authoritative book provides a stimulus to research the oscillatory and asymptotic properties of these equations. It examines equations of first, second, and higher orders as well as the asymptotic behavior for tending toward infinity. These results are then generalized for partial differential equations of neutral type. The book also describes the historical development of the field and discusses applications in mathematical models of processes and phenomena in physics, electrical control and engineering, physical chemistry, and mathematical biology. This book is an important tool not only for mathematicians, but also for specialists in many fields including physicists, engineers, and biologists. It may be used as a graduate-level textbook or as a reference book for a wide range of subjects, from radiophysics to electrical and control engineering to biological science.

Functional Spaces for the Theory of Elliptic Partial Differential Equations

Author : Françoise Demengel
Publisher : Springer Science & Business Media
ISBN 13 : 1447128079
Total Pages : 465 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Functional Spaces for the Theory of Elliptic Partial Differential Equations by : Françoise Demengel

Download or read book Functional Spaces for the Theory of Elliptic Partial Differential Equations written by Françoise Demengel and published by Springer Science & Business Media. This book was released on 2012-01-24 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions. This book offers on the one hand a complete theory of Sobolev spaces, which are of fundamental importance for elliptic linear and non-linear differential equations, and explains on the other hand how the abstract methods of convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems. The book also considers other kinds of functional spaces which are useful for treating variational problems such as the minimal surface problem. The main purpose of the book is to provide a tool for graduate and postgraduate students interested in partial differential equations, as well as a useful reference for researchers active in the field. Prerequisites include a knowledge of classical analysis, differential calculus, Banach and Hilbert spaces, integration and the related standard functional spaces, as well as the Fourier transformation on the Schwartz space. There are complete and detailed proofs of almost all the results announced and, in some cases, more than one proof is provided in order to highlight different features of the result. Each chapter concludes with a range of exercises of varying levels of difficulty, with hints to solutions provided for many of them.

Introduction to the Theory and Applications of Functional Differential Equations

Author : V. Kolmanovskii
Publisher : Springer Science & Business Media
ISBN 13 : 9401719659
Total Pages : 648 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Introduction to the Theory and Applications of Functional Differential Equations by : V. Kolmanovskii

Download or read book Introduction to the Theory and Applications of Functional Differential Equations written by V. Kolmanovskii and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the most important issues in the theory of functional differential equations and their applications for both deterministic and stochastic cases. Among the subjects treated are qualitative theory, stability, periodic solutions, optimal control and estimation, the theory of linear equations, and basic principles of mathematical modelling. The work, which treats many concrete problems in detail, gives a good overview of the entire field and will serve as a stimulating guide to further research. Audience: This volume will be of interest to researchers and (post)graduate students working in analysis, and in functional analysis in particular. It will also appeal to mathematical engineers, industrial mathematicians, mathematical system theoreticians and mathematical modellers.

Functional Integration and Partial Differential Equations. (AM-109), Volume 109

Author : Mark Iosifovich Freidlin
Publisher : Princeton University Press
ISBN 13 : 1400881595
Total Pages : 560 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Functional Integration and Partial Differential Equations. (AM-109), Volume 109 by : Mark Iosifovich Freidlin

Download or read book Functional Integration and Partial Differential Equations. (AM-109), Volume 109 written by Mark Iosifovich Freidlin and published by Princeton University Press. This book was released on 2016-03-02 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses some aspects of the theory of partial differential equations from the viewpoint of probability theory. It is intended not only for specialists in partial differential equations or probability theory but also for specialists in asymptotic methods and in functional analysis. It is also of interest to physicists who use functional integrals in their research. The work contains results that have not previously appeared in book form, including research contributions of the author.