Oscillation Theory Of Delay Differential Equations
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Oscillation Theory Of Delay Differential Equations
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Author : I. Győri
language : en
Publisher: Clarendon Press
Release Date : 1991
Oscillation Theory Of Delay Differential Equations written by I. Győri and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
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 Neutral Differential Equations With Delay
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Author : D.D Bainov
language : en
Publisher: CRC Press
Release Date : 1991-01-01
Oscillation Theory For Neutral Differential Equations With Delay written by D.D Bainov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-01 with Mathematics categories.
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 For Functional Differential Equations
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Author : Lynn Erbe
language : en
Publisher: Routledge
Release Date : 2017-10-02
Oscillation Theory For Functional Differential Equations written by Lynn Erbe and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-02 with Mathematics categories.
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.
Oscillation Theory Of Delay Differential Equations With Applications
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Author : I. Györi
language : en
Publisher:
Release Date : 2023
Oscillation Theory Of Delay Differential Equations With Applications written by I. Györi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Differential equations categories.
The aim of this monograph is to present an account of the advances in the oscillation theory of delay differential equations - considering applications as diverse as the populations of blowflies, logistic equations in ecology and the survival of red blood cells in animals.
Nonoscillation And Oscillation Theory For Functional Differential Equations
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Author : Ravi P. Agarwal
language : en
Publisher: CRC Press
Release Date : 2004-08-30
Nonoscillation And Oscillation Theory For Functional Differential Equations written by Ravi P. Agarwal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-30 with Mathematics categories.
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 Difference And Functional Differential Equations
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Author : R.P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Oscillation Theory For Difference And Functional Differential Equations written by R.P. Agarwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
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.
Oscillation And Dynamics In Delay Equations
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Author : John R. Graef
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Oscillation And Dynamics In Delay Equations written by John R. Graef and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
Oscillation theory and dynamical systems have long been rich and active areas of research. Containing frontier contributions by some of the leaders in the field, this book brings together papers based on presentations at the AMS meeting in San Francisco in January, 1991. With special emphasis on delay equations, the papers cover a broad range of topics in ordinary, partial, and difference equations and include applications to problems in commodity prices, biological modeling, and number theory. The book would be of interest to graduate students and researchers in mathematics or those in other fields who have an interest in delay equations and their applications.
Oscillation Theory Of Differential Equations With Deviating Arguments
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Author : G. S. Ladde
language : en
Publisher: Marcel Dekker
Release Date : 1987
Oscillation Theory Of Differential Equations With Deviating Arguments written by G. S. Ladde and has been published by Marcel Dekker this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Differential equations categories.
Theory Of Third Order Differential Equations
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Author : Seshadev Padhi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-16
Theory Of Third Order Differential Equations written by Seshadev Padhi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-16 with Mathematics categories.
This book discusses the theory of third-order differential equations. Most of the results are derived from the results obtained for third-order linear homogeneous differential equations with constant coefficients. M. Gregus, in his book written in 1987, only deals with third-order linear differential equations. These findings are old, and new techniques have since been developed and new results obtained. Chapter 1 introduces the results for oscillation and non-oscillation of solutions of third-order linear differential equations with constant coefficients, and a brief introduction to delay differential equations is given. The oscillation and asymptotic behavior of non-oscillatory solutions of homogeneous third-order linear differential equations with variable coefficients are discussed in Ch. 2. The results are extended to third-order linear non-homogeneous equations in Ch. 3, while Ch. 4 explains the oscillation and non-oscillation results for homogeneous third-order nonlinear differential equations. Chapter 5 deals with the z-type oscillation and non-oscillation of third-order nonlinear and non-homogeneous differential equations. Chapter 6 is devoted to the study of third-order delay differential equations. Chapter 7 explains the stability of solutions of third-order equations. Some knowledge of differential equations, analysis and algebra is desirable, but not essential, in order to study the topic.
Discrete Oscillation Theory
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Author : Ravi P. Agarwal
language : en
Publisher: Hindawi Publishing Corporation
Release Date : 2005
Discrete Oscillation Theory written by Ravi P. Agarwal and has been published by Hindawi Publishing Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Difference Equations categories.
This book is devoted to a rapidly developing branch of the qualitative theory of difference equations with or without delays. It presents the theory of oscillation of difference equations, exhibiting classical as well as very recent results in that area. While there are several books on difference equations and also on oscillation theory for ordinary differential equations, there is until now no book devoted solely to oscillation theory for difference equations. This book is filling the gap, and it can easily be used as an encyclopedia and reference tool for discrete oscillation theory. In nine chapters, the book covers a wide range of subjects, including oscillation theory for second-order linear difference equations, systems of difference equations, half-linear difference equations, nonlinear difference equations, neutral difference equations, delay difference equations, and differential equations with piecewise constant arguments. This book summarizes almost 300 recent research papers and hence covers all aspects of discrete oscillation theory that have been discussed in recent journal articles. The presented theory is illustrated with 121 examples throughout the book. Each chapter concludes with a section that is devoted to notes and bibliographical and historical remarks. The book is addressed to a wide audience of specialists such as mathematicians, engineers, biologists, and physicists. Besides serving as a reference tool for researchers in difference equations, this book can also be easily used as a textbook for undergraduate or graduate classes. It is written at a level easy to understand for college students who have had courses in calculus.