Comparison And Oscillation Theory Of Linear Differential Equations

Author : C. A. Swanson
Publisher : Elsevier
Page : 238 pages
File Size : 47,6 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9781483266671

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Comparison and Oscillation Theory of Linear Differential Equations by C. A. Swanson Pdf

Mathematics in Science and Engineering, Volume 48: Comparison and Oscillation Theory of Linear Differential Equations deals primarily with the zeros of solutions of linear differential equations. This volume contains five chapters. Chapter 1 focuses on comparison theorems for second order equations, while Chapter 2 treats oscillation and nonoscillation theorems for second order equations. Separation, comparison, and oscillation theorems for fourth order equations are covered in Chapter 3. In Chapter 4, ordinary equations and systems of differential equations are reviewed. The last chapter discusses the result of the first analog of a Sturm-type comparison theorem for an elliptic partial differential equation. This publication is intended for college seniors or beginning graduate students who are well-acquainted with advanced calculus, complex analysis, linear algebra, and linear differential equations.

Author : R.P. Agarwal,Said R. Grace,Donal O'Regan
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 50,5 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 : Anatoli Torokhti,Phil Howlett
Publisher : Elsevier Science Limited
Page : 322 pages
File Size : 40,5 Mb
Release : 1968
Category : Mathematics
ISBN : 0126789509

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Computational Methods for Modeling of Nonlinear Systems by Anatoli Torokhti,Phil Howlett Pdf

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Author : Lynn Erbe
Publisher : Routledge
Page : 230 pages
File Size : 51,9 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
Publisher : Hindawi Publishing Corporation
Page : 977 pages
File Size : 45,7 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 : Ondrej Dosly,Pavel Rehak
Publisher : Elsevier
Page : 533 pages
File Size : 46,5 Mb
Release : 2005-07-06
Category : Mathematics
ISBN : 9780080461236

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Half-Linear Differential Equations by Ondrej Dosly,Pavel Rehak Pdf

The book presents a systematic and compact treatment of the qualitative theory of half-linear differential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE’s with p-Laplacian, half-linear difference equations and various more general nonlinear differential equations. - The first complete treatment of the qualitative theory of half-linear differential equations. - Comparison of linear and half-linear theory. - Systematic approach to half-linear oscillation and asymptotic theory. - Comprehensive bibliography and index. - Useful as a reference book in the topic.

Author : R.P. Agarwal,Said R. Grace,Donal O'Regan
Publisher : Springer Science & Business Media
Page : 685 pages
File Size : 50,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401725156

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Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations by R.P. Agarwal,Said R. Grace,Donal O'Regan Pdf

In this monograph, the authors present a compact, thorough, systematic, and self-contained oscillation theory for linear, half-linear, superlinear, and sublinear second-order ordinary differential equations. An important feature of this monograph is the illustration of several results with examples of current interest. This book will stimulate further research into oscillation theory. This book is written at a graduate level, and is intended for university libraries, graduate students, and researchers working in the field of ordinary differential equations.

Author : I. Győri,G. E. Ladas
Publisher : Clarendon Press
Page : 392 pages
File Size : 43,6 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 : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 43,9 Mb
Release : 1703
Category : Electronic
ISBN : OCLC:211561040

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Copyen van eenige stucken door mr. Nicolaas Listing advocaat [...] in de proceduren, die hy al verder genootsaakt werd te moeten voeren tegen Meynard Domp by Anonim Pdf

Author : Ravi P. Agarwal,Martin Bohner,Wan-Tong Li
Publisher : CRC Press
Page : 400 pages
File Size : 55,9 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 : Uri Elias
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 50,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401725170

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Oscillation Theory of Two-Term Differential Equations by Uri Elias Pdf

Oscillation theory was born with Sturm's work in 1836. It has been flourishing for the past fifty years. Nowadays it is a full, self-contained discipline, turning more towards nonlinear and functional differential equations. Oscillation theory flows along two main streams. The first aims to study prop erties which are common to all linear differential equations. The other restricts its area of interest to certain families of equations and studies in maximal details phenomena which characterize only those equations. Among them we find third and fourth order equations, self adjoint equations, etc. Our work belongs to the second type and considers two term linear equations modeled after y(n) + p(x)y = O. More generally, we investigate LnY + p(x)y = 0, where Ln is a disconjugate operator and p(x) has a fixed sign. These equations enjoy a very rich structure and are the natural generalization of the Sturm-Liouville operator. Results about such equations are distributed over hundreds of research papers, many of them are reinvented again and again and the same phenomenon is frequently discussed from various points of view and different definitions of the authors. Our aim is to introduce an order into this plenty and arrange it in a unified and self contained way. The results are readapted and presented in a unified approach. In many cases completely new proofs are given and in no case is the original proof copied verbatim. Many new results are included.

Author : G. S. Ladde,V. Lakshmikantham,B. G. Zhang
Publisher : Marcel Dekker
Page : 328 pages
File Size : 43,5 Mb
Release : 1987
Category : Mathematics
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 : K. Kreith
Publisher : Springer
Page : 115 pages
File Size : 41,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540400059

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Oscillation Theory by K. Kreith Pdf

Author : D.D Bainov,D.P Mishev
Publisher : CRC Press
Page : 296 pages
File Size : 53,5 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 : Drumi D Bainov,Dimitar P Mishev
Publisher : World Scientific
Page : 218 pages
File Size : 48,7 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.