Theory Of Differential Equations With Unbounded Delay

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Theory of Differential Equations with Unbounded Delay

Author : V. Lakshmikantham
Publisher : Springer Science & Business Media
ISBN 13 : 146152606X
Total Pages : 390 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Theory of Differential Equations with Unbounded Delay by : V. Lakshmikantham

Download or read book Theory of Differential Equations with Unbounded Delay written by V. Lakshmikantham and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Because the theory of equations with delay terms occurs in a variety of contexts, it is important to provide a framework, whenever possible, to handle as many cases as possible simultaneously so as to bring out a better insight and understanding of the subtle differences of the various equations with delays. Furthermore, such a unified theory would avoid duplication and expose open questions that are significant for future research. It is in this spirit that the authors view the importance of their monograph, which presents a systematic and unified theory of recent developments of equations with unbounded delay, describes the current state of the theory showing the essential unity achieved, and provides a general structure applicable to a variety of problems. It is the first book that: (i) presents a unified framework to investigate the basic existence theory for a variety of equations with delay; (ii) treats the classification of equations with memory precisely so as to bring out the subtle differences between them; (iii) develops a systematic study of stability theory in terms of two different measures which includes several known concepts; and (iv) exhibits the advantages of employing Lyapunov functions on product spaces as well as the method of perturbing Lyapunov functions. This book will be of value to researchers and advanced graduate students in mathematics, electrical engineering and biomathematics.

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 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.

Oscillation Theory of Delay Differential Equations

Author : I. Győri
Publisher : Clarendon Press
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Oscillation Theory of Delay Differential Equations by : I. Győri

Download or read book Oscillation Theory of Delay Differential Equations written by I. Győri and published by Clarendon Press. This book was released on 1991 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been a resurgence of interest in the study of delay differential equations motivated largely by new applications in physics, biology, ecology, and physiology. The aim of this monograph is to present a reasonably self-contained account of the advances in the oscillation theory of this class of equations. Throughout, the main topics of study are shown in action, with applications to such diverse problems as insect population estimations, logistic equations in ecology, the survival of red blood cells in animals, integro-differential equations, and the motion of the tips of growing plants. The authors begin by reviewing the basic theory of delay differential equations, including the fundamental results of existence and uniqueness of solutions and the theory of the Laplace and z-transforms. Little prior knowledge of the subject is required other than a firm grounding in the main techniques of differential equation theory. As a result, this book provides an invaluable reference to the recent work both for mathematicians and for all those whose research includes the study of this fascinating class of differential equations.

Oscillation Theory for Functional Differential Equations

Author : Lynn Erbe
Publisher : Routledge
ISBN 13 : 1351426311
Total Pages : 230 pages
Book Rating : 4.3/5 (514 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 Routledge. This book was released on 2017-10-02 with total page 230 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.

Basic Theory Of Fractional Differential Equations (Third Edition)

Author : Yong Zhou
Publisher : World Scientific
ISBN 13 : 9811271704
Total Pages : 516 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Basic Theory Of Fractional Differential Equations (Third Edition) by : Yong Zhou

Download or read book Basic Theory Of Fractional Differential Equations (Third Edition) written by Yong Zhou and published by World Scientific. This book was released on 2023-10-06 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary differential equations and evolution equations. It is self-contained and unified in presentation, and provides the readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, Picard operators technique, critical point theory and semigroups theory. This book is based on the research work done so far by the author and other experts, and contains comprehensive up-to-date materials on the topic.In this third edition, four new topics have been added: Hilfer fractional evolution equations and infinite interval problems, oscillations and nonoscillations, fractional Hamiltonian systems, fractional Rayleigh-Stokes equations, and wave equations. The bibliography has also been updated and expanded.This book is useful to researchers, graduate or PhD students dealing with fractional calculus and applied analysis, differential equations, and related areas of research.

Ordinary and Delay Differential Equations

Author : R. D. Driver
Publisher : Springer Science & Business Media
ISBN 13 : 1468494678
Total Pages : 513 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Ordinary and Delay Differential Equations by : R. D. Driver

Download or read book Ordinary and Delay Differential Equations written by R. D. Driver and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is designed for the intermediate-level course on ordinary differential equations offered at many universities and colleges. It treats, as standard topics of such a course: existence and uniqueness theory, linear s- terns, stability theory, and introductory phase-plane analysis of autonomous second order systems. The unique feature of the book is its further inc- sion of a substantial introduction to delay differential eq- tions. Such equations are motivated by problems in control theory, physics, biology, ecology, economics, inventory c- trol, and the theory of nuclear reactors. The surge of interest in delay differential equations during the past two or three decades is evidenced by th- sands of research papers on the subject and about 20 published books devoted in whole or in part to these equations. The v * ... books include those of Myskis [1951], El' sgol' c [1955] and [1964], Pinney [1958], Krasovskil [1959], Bellman and Cooke [1963], Norkin [1965], Halanay [1966], Oguztoreli [1966], Lakshmikantham and Leela [1969], Mitropol'skir and Martynjuk [1969], Martynjuk [1971], and Hale [1971], plus a number of symposium and seminar proceedings published in the U.S. and the U.S.S.R. These books have influenced the present textbook.

Systems with Delays

Author : A. V. Kim
Publisher : John Wiley & Sons
ISBN 13 : 1119117720
Total Pages : 184 pages
Book Rating : 4.1/5 (191 download)

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Book Synopsis Systems with Delays by : A. V. Kim

Download or read book Systems with Delays written by A. V. Kim and published by John Wiley & Sons. This book was released on 2015-07-23 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main aim of the book is to present new constructive methods of delay differential equation (DDE) theory and to give readers practical tools for analysis, control design and simulating of linear systems with delays. Referred to as “systems with delays” in this volume, this class of differential equations is also called delay differential equations (DDE), time-delay systems, hereditary systems, and functional differential equations. Delay differential equations are widely used for describing and modeling various processes and systems in different applied problems At present there are effective control and numerical methods and corresponding software for analysis and simulating different classes of ordinary differential equations (ODE) and partial differential equations (PDE). There are many applications for these types of equations, because of this progress, but there are not as many methodologies in systems with delays that are easily applicable for the engineer or applied mathematician. there are no methods of finding solutions in explicit forms, and there is an absence of generally available general-purpose software packages for simulating such systems. Systems with Delays fills this void and provides easily applicable methods for engineers, mathematicians, and scientists to work with delay differential equations in their operations and research.

Theory of Impulsive Differential Equations

Author : V. Lakshmikantham
Publisher : World Scientific
ISBN 13 : 9789971509705
Total Pages : 296 pages
Book Rating : 4.5/5 (97 download)

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Book Synopsis Theory of Impulsive Differential Equations by : V. Lakshmikantham

Download or read book Theory of Impulsive Differential Equations written by V. Lakshmikantham and published by World Scientific. This book was released on 1989 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many evolution processes are characterized by the fact that at certain moments of time they experience a change of state abruptly. These processes are subject to short-term perturbations whose duration is negligible in comparison with the duration of the process. Consequently, it is natural to assume that these perturbations act instantaneously, that is, in the form of impulses. It is known, for example, that many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, pharmacokinetics and frequency modulated systems, do exhibit impulsive effects. Thus impulsive differential equations, that is, differential equations involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems.

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, Nonoscillation, Stability and Asymptotic Properties for Second and Higher Order Functional Differential Equations

Author : Leonid Berezansky
Publisher : CRC Press
ISBN 13 : 1000048632
Total Pages : 488 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Oscillation, Nonoscillation, Stability and Asymptotic Properties for Second and Higher Order Functional Differential Equations by : Leonid Berezansky

Download or read book Oscillation, Nonoscillation, Stability and Asymptotic Properties for Second and Higher Order Functional Differential Equations written by Leonid Berezansky and published by CRC Press. This book was released on 2020-05-18 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic properties of solutions such as stability/ instability,oscillation/ nonoscillation, existence of solutions with specific asymptotics, maximum principles present a classical part in the theory of higher order functional differential equations. The use of these equations in applications is one of the main reasons for the developments in this field. The control in the mechanical processes leads to mathematical models with second order delay differential equations. Stability and stabilization of second order delay equations are one of the main goals of this book. The book is based on the authors’ results in the last decade. Features: Stability, oscillatory and asymptotic properties of solutions are studied in correlation with each other. The first systematic description of stability methods based on the Bohl-Perron theorem. Simple and explicit exponential stability tests. In this book, various types of functional differential equations are considered: second and higher orders delay differential equations with measurable coefficients and delays, integro-differential equations, neutral equations, and operator equations. Oscillation/nonoscillation, existence of unbounded solutions, instability, special asymptotic behavior, positivity, exponential stability and stabilization of functional differential equations are studied. New methods for the study of exponential stability are proposed. Noted among them inlcude the W-transform (right regularization), a priory estimation of solutions, maximum principles, differential and integral inequalities, matrix inequality method, and reduction to a system of equations. The book can be used by applied mathematicians and as a basis for a course on stability of functional differential equations for graduate students.

Functional Differential Equations

Author : Constantin Corduneanu
Publisher : John Wiley & Sons
ISBN 13 : 1119189470
Total Pages : 362 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 2016-04-11 with total page 362 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.

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

Delay Equations

Author : Odo Diekmann
Publisher : Springer Science & Business Media
ISBN 13 : 1461242061
Total Pages : 547 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Delay Equations by : Odo Diekmann

Download or read book Delay Equations written by Odo Diekmann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim here is to provide an introduction to the mathematical theory of infinite dimensional dynamical systems by focusing on a relatively simple - yet rich - class of examples, delay differential equations. This textbook contains detailed proofs and many exercises, intended both for self-study and for courses at graduate level, as well as a reference for basic results. As the subtitle indicates, this book is about concepts, ideas, results and methods from linear functional analysis, complex function theory, the qualitative theory of dynamical systems and nonlinear analysis. The book provides the reader with a working knowledge of applied functional analysis and dynamical systems.

Recent Developments in Mathematical, Statistical and Computational Sciences

Author : D. Marc Kilgour
Publisher : Springer Nature
ISBN 13 : 3030635910
Total Pages : 728 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Recent Developments in Mathematical, Statistical and Computational Sciences by : D. Marc Kilgour

Download or read book Recent Developments in Mathematical, Statistical and Computational Sciences written by D. Marc Kilgour and published by Springer Nature. This book was released on 2021-08-29 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes an up-to-date account of principles, methods, and tools for mathematical and statistical modelling in a wide range of research fields, including medicine, health sciences, biology, environmental science, engineering, physics, chemistry, computation, finance, economics, and social sciences. It presents original solutions to real-world problems, emphasizes the coordinated development of theories and applications, and promotes interdisciplinary collaboration among mathematicians, statisticians, and researchers in other disciplines. Based on a highly successful meeting, the International Conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2019, held from August 18 to 23, 2019, on the main campus of Wilfrid Laurier University, Waterloo, Canada, the contributions are the results of submissions from the conference participants. They provide readers with a broader view of the methods, ideas and tools used in mathematical, statistical and computational sciences.

Lyapunov Functionals and Stability of Stochastic Functional Differential Equations

Author : Leonid Shaikhet
Publisher : Springer Science & Business Media
ISBN 13 : 3319001019
Total Pages : 352 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Lyapunov Functionals and Stability of Stochastic Functional Differential Equations by : Leonid Shaikhet

Download or read book Lyapunov Functionals and Stability of Stochastic Functional Differential Equations written by Leonid Shaikhet and published by Springer Science & Business Media. This book was released on 2013-03-29 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for difference equations with discrete and continuous time. The text begins with both a description and a delineation of the peculiarities of deterministic and stochastic functional differential equations. There follows basic definitions for stability theory of stochastic hereditary systems, and the formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of different mathematical models such as: • inverted controlled pendulum; • Nicholson's blowflies equation; • predator-prey relationships; • epidemic development; and • mathematical models that describe human behaviours related to addictions and obesity. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations is primarily addressed to experts in stability theory but will also be of interest to professionals and students in pure and computational mathematics, physics, engineering, medicine, and biology.

Functional Equations with Causal Operators

Author : C. Corduneanu
Publisher : CRC Press
ISBN 13 : 020316637X
Total Pages : 185 pages
Book Rating : 4.2/5 (31 download)

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Book Synopsis Functional Equations with Causal Operators by : C. Corduneanu

Download or read book Functional Equations with Causal Operators written by C. Corduneanu and published by CRC Press. This book was released on 2002-09-05 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with cau