Oscillation Theory For Neutral Differential Equations With Delay

Author : D.D Bainov,D.P Mishev
Publisher : CRC Press
Page : 296 pages
File Size : 44,7 Mb
Release : 1991-01-01
Category : Mathematics
ISBN : 0750301422

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Oscillation Theory for Neutral Differential Equations with Delay by D.D Bainov,D.P Mishev Pdf

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.

Author : I. Győri,G. E. Ladas
Publisher : Clarendon Press
Page : 392 pages
File Size : 49,9 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:39015025010995

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Oscillation Theory of Delay Differential Equations by I. Győri,G. E. Ladas Pdf

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.

Author : Lynn Erbe
Publisher : Routledge
Page : 230 pages
File Size : 52,8 Mb
Release : 2017-10-02
Category : Mathematics
ISBN : 9781351426312

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Oscillation Theory for Functional Differential Equations by Lynn Erbe Pdf

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.

Author : Ravi P. Agarwal,Martin Bohner,Wan-Tong Li
Publisher : CRC Press
Page : 400 pages
File Size : 48,6 Mb
Release : 2004-08-30
Category : Mathematics
ISBN : 9780203025741

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Nonoscillation and Oscillation Theory for Functional Differential Equations by Ravi P. Agarwal,Martin Bohner,Wan-Tong Li Pdf

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

Author : R.P. Agarwal,Said R. Grace,Donal O'Regan
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 54,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401594011

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Oscillation Theory for Difference and Functional Differential Equations by R.P. Agarwal,Said R. Grace,Donal O'Regan Pdf

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.

Author : John R. Graef,Jack K. Hale
Publisher : American Mathematical Soc.
Page : 263 pages
File Size : 40,5 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821851401

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Oscillation and Dynamics in Delay Equations by John R. Graef,Jack K. Hale Pdf

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.

Author : I. Györi,Gerasimos Ladas
Publisher : Unknown
Page : 0 pages
File Size : 44,5 Mb
Release : 2023
Category : Differential equations
ISBN : 1383025770

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Oscillation Theory of Delay Differential Equations with . Applications by I. Györi,Gerasimos Ladas Pdf

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.

Author : G. S. Ladde,V. Lakshmikantham,B. G. Zhang
Publisher : Marcel Dekker
Page : 328 pages
File Size : 51,5 Mb
Release : 1987
Category : Differential equations
ISBN : UCAL:B4405926

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Oscillation Theory of Differential Equations with Deviating Arguments by G. S. Ladde,V. Lakshmikantham,B. G. Zhang Pdf

Author : Leonid Berezansky,Alexander Domoshnitsky,Roman Koplatadze
Publisher : CRC Press
Page : 488 pages
File Size : 42,5 Mb
Release : 2020-05-18
Category : Mathematics
ISBN : 9781000048636

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Oscillation, Nonoscillation, Stability and Asymptotic Properties for Second and Higher Order Functional Differential Equations by Leonid Berezansky,Alexander Domoshnitsky,Roman Koplatadze Pdf

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.

Author : Ravi P. Agarwal,Leonid Berezansky,Elena Braverman,Alexander Domoshnitsky
Publisher : Springer Science & Business Media
Page : 526 pages
File Size : 53,5 Mb
Release : 2012-04-23
Category : Mathematics
ISBN : 9781461434559

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Nonoscillation Theory of Functional Differential Equations with Applications by Ravi P. Agarwal,Leonid Berezansky,Elena Braverman,Alexander Domoshnitsky Pdf

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.​

Author : Ravi P. Agarwal
Publisher : Hindawi Publishing Corporation
Page : 977 pages
File Size : 52,8 Mb
Release : 2005
Category : Difference Equations
ISBN : 9789775945198

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Discrete Oscillation Theory by Ravi P. Agarwal Pdf

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.

Author : Drumi D Bainov,Dimitar P Mishev
Publisher : World Scientific
Page : 218 pages
File Size : 49,6 Mb
Release : 1995-08-31
Category : Mathematics
ISBN : 9789814505253

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Oscillation Theory Of Operator-differential Equations by Drumi D Bainov,Dimitar P Mishev Pdf

In this book, the authors aim at expounding a sufficiently rich oscillation theory and asymptotic theory of operator-differential equations. This book will be of interest not only to mathematicians, but also to experts in other areas of science and technology due to the numerous applications of the results discussed in the book.

Author : Feliz Manuel Minhós,João Fialho
Publisher : MDPI
Page : 158 pages
File Size : 53,6 Mb
Release : 2021-04-15
Category : Mathematics
ISBN : 9783036507101

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Nonlinear Differential Equations and Dynamical Systems by Feliz Manuel Minhós,João Fialho Pdf

This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.

Author : Mahmut Reyhanoglu
Publisher : BoD – Books on Demand
Page : 276 pages
File Size : 50,8 Mb
Release : 2017-03-15
Category : Mathematics
ISBN : 9789535130154

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Dynamical Systems by Mahmut Reyhanoglu Pdf

There has been a considerable progress made during the recent past on mathematical techniques for studying dynamical systems that arise in science and engineering. This progress has been, to a large extent, due to our increasing ability to mathematically model physical processes and to analyze and solve them, both analytically and numerically. With its eleven chapters, this book brings together important contributions from renowned international researchers to provide an excellent survey of recent advances in dynamical systems theory and applications. The first section consists of seven chapters that focus on analytical techniques, while the next section is composed of four chapters that center on computational techniques.

Author : Ravi P. Agarwal,Said R. Grace,Donal O'Regan
Publisher : CRC Press
Page : 416 pages
File Size : 51,5 Mb
Release : 2002-11-21
Category : Mathematics
ISBN : 9780203222898

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Oscillation Theory for Second Order Dynamic Equations by Ravi P. Agarwal,Said R. Grace,Donal O'Regan Pdf

The qualitative theory of dynamic equations is a rapidly developing area of research. In the last 50 years, the Oscillation Theory of ordinary, functional, neutral, partial and impulsive differential equations, and their discrete versions, has inspired many scholars. Hundreds of research papers have been published in every major mathematical journa