Theory of Functional Differential Equations

Theory of Functional Differential Equations

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.

Author: Jack K. Hale

Publisher: Springer Science & Business Media

ISBN: 9781461298922

Category: Mathematics

Page: 366

View: 727

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.
Categories: Mathematics

Bifurcation Theory of Functional Differential Equations

Bifurcation Theory of Functional Differential Equations

This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs).

Author: Shangjiang Guo

Publisher: Springer Science & Business Media

ISBN: 9781461469926

Category: Mathematics

Page: 289

View: 426

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).
Categories: Mathematics

Oscillation Theory for Functional Differential Equations

Oscillation Theory for Functional Differential Equations

The book shows how to extend the techniques for boundary value problems of ordinary differential equations to those of functional differential equations.

Author: Lynn Erbe

Publisher: Routledge

ISBN: 9781351426329

Category: Mathematics

Page: 504

View: 854

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.
Categories: Mathematics

Nonoscillation Theory of Functional Differential Equations with Applications

Nonoscillation Theory of Functional Differential Equations with Applications

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.​

Author: Ravi P. Agarwal

Publisher: Springer Science & Business Media

ISBN: 9781461434559

Category: Mathematics

Page: 520

View: 131

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.​
Categories: Mathematics

Functional Differential Equations

Functional Differential Equations

Together these books form a powerful library for this intriguing field of modern analysis.

Author: A. B. Antonevich

Publisher: CRC Press

ISBN: 0582100496

Category: Mathematics

Page: 400

View: 404

Together with the authors' Volume I. C*-Theory, the two parts comprising Functional Differential Equations: II. C*-Applications form a masterful work-the first thorough, up-to-date exposition of this field of modern analysis lying between differential equations and C*-algebras. The two parts of Volume II contain the applications of the C*-structures and theory developed in Volume I. They show the technique of using the C*-results in the study of the solvability conditions of non-local functional differential equations and demonstrate the fundamental principles underlying the interrelations between C* and functional differential objects. The authors focus on non-local pseudodifferential, singular integral, and Toeplitz operators-with continuous and piecewise continuous coefficients-convolution type operators with oscillating coefficients and shifts, and operators associated with non-local boundary value problems containing transformation operators of an argument on the boundary. They build the symbolic calculus for all these classes of operators, use it to treat concrete examples of non-local operators, present the explicit computation of their Fredholmity conditions and the index formulae, and obtain a number of related results. Part 1: Equations with Continuous Coefficients and Part 2: Equations with Discontinuous Coefficients and Boundary Value Problems can each stand alone and prove a valuable resource for researchers and students interested in operator algebraic methods in the theory of functional differential equations, and to pure C*-algebraists looking for important and promising new applications. Together these books form a powerful library for this intriguing field of modern analysis.
Categories: Mathematics

Introduction to Functional Differential Equations

Introduction to Functional Differential Equations

The present book builds upon an earlier work of J. Hale, "Theory of Func tional Differential Equations" published in 1977.

Author: Jack K. Hale

Publisher: Springer

ISBN: 1461287413

Category: Mathematics

Page: 450

View: 645

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 . . . . . . . . . . . .
Categories: Mathematics

Introduction to the Theory and Applications of Functional Differential Equations

Introduction to the Theory and Applications of Functional Differential Equations

This book covers the most important issues in the theory of functional differential equations and their applications for both deterministic and stochastic cases.

Author: V. Kolmanovskii

Publisher: Springer Science & Business Media

ISBN: 9789401719650

Category: Mathematics

Page: 648

View: 555

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.
Categories: Mathematics

Applied Theory of Functional Differential Equations

Applied Theory of Functional Differential Equations

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.

Author: V. Kolmanovskii

Publisher: Springer Science & Business Media

ISBN: 9789401580847

Category: Mathematics

Page: 234

View: 364

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.
Categories: Mathematics

Theory and Applications of Partial Functional Differential Equations

Theory and Applications of Partial Functional Differential Equations

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.

Author: Jianhong Wu

Publisher: Springer Science & Business Media

ISBN: 9781461240501

Category: Mathematics

Page: 432

View: 408

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.
Categories: Mathematics

Oscillation Theory for Difference and Functional Differential Equations

Oscillation Theory for 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.

Author: R.P. Agarwal

Publisher: Springer Science & Business Media

ISBN: 9789401594011

Category: Mathematics

Page: 338

View: 180

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.
Categories: Mathematics

Functional Differential Equations with Infinite Delay

Functional Differential Equations with Infinite Delay

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.

Author: Yoshiyuki Hino

Publisher: Springer

ISBN: 9783540473886

Category: Mathematics

Page: 318

View: 697

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.
Categories: Mathematics

Nonoscillation and Oscillation Theory for Functional Differential Equations

Nonoscillation and Oscillation Theory for Functional Differential Equations

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.

Author: Ravi P. Agarwal

Publisher: CRC Press

ISBN: 9780203025741

Category: Mathematics

Page: 400

View: 870

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
Categories: Mathematics

Stability Periodic Solutions of Ordinary Functional Differential Equations

Stability   Periodic Solutions of Ordinary   Functional Differential Equations

This book's discussion of a broad class of differential equations includes linear differential and integrodifferential equations, fixed-point theory, and the basic stability and periodicity theory for nonlinear ordinary and functional ...

Author: T. A. Burton

Publisher: Courier Corporation

ISBN: 9780486150451

Category: Mathematics

Page: 352

View: 842

This book's discussion of a broad class of differential equations includes linear differential and integrodifferential equations, fixed-point theory, and the basic stability and periodicity theory for nonlinear ordinary and functional differential equations.
Categories: Mathematics

Introduction to the Theory of Functional Differential Equations

Introduction to the Theory of Functional Differential Equations

The book covers many topics in the theory of functionaldifferential equations: key questions of the general theory, boundary value problems (both linear and nonlinear), controlproblems (with both classic and impulse control), ...

Author:

Publisher:

ISBN: 9774540646

Category: Control theory

Page: 324

View: 266

This book covers many topics in the theory of functional differential equations: key questions of the general theory, boundary value problems (both linear and nonlinear), control problems (with both classic and impulse control), stability problems, calculus of variations problems, computer-assisted techniques for studying the problems mentioned.
Categories: Control theory

Stability by Fixed Point Theory for Functional Differential Equations

Stability by Fixed Point Theory for Functional Differential Equations

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.

Author: T. A. Burton

Publisher: Courier Corporation

ISBN: 9780486153322

Category: Mathematics

Page: 368

View: 186

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.
Categories: Mathematics

Introduction to Functional Differential Equations

Introduction to Functional Differential Equations

The present book builds upon an earlier work of J. Hale, "Theory of Func tional Differential Equations" published in 1977.

Author: Jack K. Hale

Publisher: Springer Science & Business Media

ISBN: 9781461243427

Category: Mathematics

Page: 450

View: 315

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 . . . . . . . . . . . .
Categories: Mathematics

Functional Differential Equations

Functional Differential Equations

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.

Author: Constantin Corduneanu

Publisher: John Wiley & Sons

ISBN: 9781119189497

Category: Mathematics

Page: 368

View: 901

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.
Categories: Mathematics

Volterra Integral and Differential Equations

Volterra Integral and Differential Equations

This book seeks to present Volterra integral and functional differential equations in that same framwork, allowing the readers to parlay their knowledge of ordinary differential equations into theory and application of the more general ...

Author: Ted A. Burton

Publisher: Elsevier

ISBN: 9780080459554

Category: Mathematics

Page: 368

View: 588

Most mathematicians, engineers, and many other scientists are well-acquainted with theory and application of ordinary differential equations. This book seeks to present Volterra integral and functional differential equations in that same framwork, allowing the readers to parlay their knowledge of ordinary differential equations into theory and application of the more general problems. Thus, the presentation starts slowly with very familiar concepts and shows how these are generalized in a natural way to problems involving a memory. Liapunov's direct method is gently introduced and applied to many particular examples in ordinary differential equations, Volterra integro-differential equations, and functional differential equations. By Chapter 7 the momentum has built until we are looking at problems on the frontier. Chapter 7 is entirely new, dealing with fundamental problems of the resolvent, Floquet theory, and total stability. Chapter 8 presents a solid foundation for the theory of functional differential equations. Many recent results on stability and periodic solutions of functional differential equations are given and unsolved problems are stated. Key Features: - Smooth transition from ordinary differential equations to integral and functional differential equations. - Unification of the theories, methods, and applications of ordinary and functional differential equations. - Large collection of examples of Liapunov functions. - Description of the history of stability theory leading up to unsolved problems. - Applications of the resolvent to stability and periodic problems. 1. Smooth transition from ordinary differential equations to integral and functional differential equations. 2. Unification of the theories, methods, and applications of ordinary and functional differential equations. 3. Large collection of examples of Liapunov functions. 4. Description of the history of stability theory leading up to unsolved problems. 5. Applications of the resolvent to stability and periodic problems.
Categories: Mathematics