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Author : Aleksandr N. Sarkovskij
Publisher :
ISBN 13 :
Total Pages : 149 pages
Book Rating : 4.:/5 (878 download)
Download or read book Asymptotic behaviour of solutions of functional differential equations written by Aleksandr N. Sarkovskij and published by . This book was released on 1978 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard Bellman
Publisher : American Mathematical Soc.
ISBN 13 : 0821812351
Total Pages : 99 pages
Book Rating : 4.8/5 (218 download)
Download or read book Asymptotic Behavior of Solutions of Differential-Difference Equations written by Richard Bellman and published by American Mathematical Soc.. This book was released on 1959 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Shuhui Wu
Publisher : GRIN Verlag
ISBN 13 : 3346600963
Total Pages : 193 pages
Book Rating : 4.3/5 (466 download)
Download or read book The Asymptotic and Oscillatory Behaviour of Difference and Differential Equations written by Shuhui Wu and published by GRIN Verlag. This book was released on 2022-03-04 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Doctoral Thesis / Dissertation from the year 2009 in the subject Mathematics - Applied Mathematics, London Metropolitan University, language: English, abstract: This thesis deals with the asymptotic and oscillatory behaviour of the solutions of certain differential and difference equations. It mainly consists of three parts. The first part is to study the asymptotic behaviour of certain differential equations. The second part is to look for oscillatory criteria for certain nonlinear neutral differential equations. And the third part is to establish new criteria for a class of nonlinear neutral difference equations of any order with continuous variable and another type of higher even order nonlinear neutral difference equations to be oscillatory. A functional differential equation is a differential equation involving the values of the unknown functions at present, as well as at past or future time. The word “time” here stands for the independent variable. In the thesis, the concept of a functional differential equation is confined to ordinary differential equations, although it suits partial ones as well. Functional differential equations can be classified into four types according to their deviations: retarded, advanced, neutral and mixed. A neutral equation is one in which derivative of functionals of the past history and the present state are involved, but no future states occur in the equation. The order of a differential equation is the order of the highest derivative of the unknown function. A difference equation is a specific type of recurrence relation, which is an equation that defines a sequence recursively: each term of the sequence is defined as a function of the preceding terms. On the other hand, difference equations can be thought of as the discrete analogue of the corresponding differential equations. By analogy with differential equations, difference equations also can be classified into four types: delay, advanced, neutral, and mixed. The order of a difference equation is the difference between the largest and the smallest values of the integer variable explicitly involved in the difference equation.
Author : John Carr (D.Phil.)
Publisher :
ISBN 13 :
Total Pages : 94 pages
Book Rating : 4.:/5 (471 download)
Download or read book The Asymptotic Behaviour of the Solutions of Some Linear Functional Differential Equations written by John Carr (D.Phil.) and published by . This book was released on 1974 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mikhail V. Fedoryuk
Publisher : Springer Science & Business Media
ISBN 13 : 3642580165
Total Pages : 370 pages
Book Rating : 4.6/5 (425 download)
Download or read book Asymptotic Analysis written by Mikhail V. Fedoryuk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we present the main results on the asymptotic theory of ordinary linear differential equations and systems where there is a small parameter in the higher derivatives. We are concerned with the behaviour of solutions with respect to the parameter and for large values of the independent variable. The literature on this question is considerable and widely dispersed, but the methods of proofs are sufficiently similar for this material to be put together as a reference book. We have restricted ourselves to homogeneous equations. The asymptotic behaviour of an inhomogeneous equation can be obtained from the asymptotic behaviour of the corresponding fundamental system of solutions by applying methods for deriving asymptotic bounds on the relevant integrals. We systematically use the concept of an asymptotic expansion, details of which can if necessary be found in [Wasow 2, Olver 6]. By the "formal asymptotic solution" (F.A.S.) is understood a function which satisfies the equation to some degree of accuracy. Although this concept is not precisely defined, its meaning is always clear from the context. We also note that the term "Stokes line" used in the book is equivalent to the term "anti-Stokes line" employed in the physics literature.
Author : Eng-bin Lim
Publisher :
ISBN 13 :
Total Pages : 110 pages
Book Rating : 4.:/5 (624 download)
Download or read book Asymptotic Behavior of Solutions of the Functional Differential Equation Xʹ(t) written by Eng-bin Lim and published by . This book was released on 1974 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Leonid Berezansky
Publisher : CRC Press
ISBN 13 : 1000048551
Total Pages : 615 pages
Book Rating : 4.0/5 ( download)
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 615 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.
Author :
Publisher :
ISBN 13 :
Total Pages : 76 pages
Book Rating : 4.:/5 (227 download)
Download or read book Asymptotic Behavior of Solutions of Differential-difference Equations written by and published by . This book was released on 1958 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the problem was considered of determining the asymptotic behavior of solutions of linear differentialdifference equations whose coefficients possess asymptotic series. Although the problem is considerably more complicated than the corresponding problem for ordinary differential equations, by means of a sequence of transformations the problem was reduced to a form where the standard techniques of ordinary differential equation theory could be employed. The differential-difference equation was transformed into an integral equation which was trans formed into an integro-differential equation. At this point the Liouville transformation plays a vital role. Although the guiding ideas were simple, the analysis became formidable. For this reason, only some of the more immediate aspects of the problem were considered.
Author : Joseph Wiener
Publisher : World Scientific
ISBN 13 : 9814505110
Total Pages : 425 pages
Book Rating : 4.8/5 (145 download)
Download or read book Generalized Solutions Of Functional Differential Equations written by Joseph Wiener and published by World Scientific. This book was released on 1993-05-28 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The need to investigate functional differential equations with discontinuous delays is addressed in this book. Recording the work and findings of several scientists on differential equations with piecewise continuous arguments over the last few years, this book serves as a useful source of reference. Great interest is placed on discussing the stability, oscillation and periodic properties of the solutions. Considerable attention is also given to the study of initial and boundary-value problems for partial differential equations of mathematical physics with discontinuous time delays. In fact, a large part of the book is devoted to the exploration of differential and functional differential equations in spaces of generalized functions (distributions) and contains a wealth of new information in this area. Each topic discussed appears to provide ample opportunity for extending the known results. A list of new research topics and open problems is also included as an update.
Author : Sigrun Bodine
Publisher : Springer
ISBN 13 : 331918248X
Total Pages : 411 pages
Book Rating : 4.3/5 (191 download)
Download or read book Asymptotic Integration of Differential and Difference Equations written by Sigrun Bodine and published by Springer. This book was released on 2015-05-26 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers in asymptotic integration as well to non-experts who are interested in the asymptotic analysis of linear differential and difference equations. It will additionally be of interest to students in mathematics, applied sciences, and engineering. Linear algebra and some basic concepts from advanced calculus are prerequisites.
Author : N.V. Azbelev
Publisher : CRC Press
ISBN 13 : 9780415269575
Total Pages : 246 pages
Book Rating : 4.2/5 (695 download)
Download or read book Stability of Differential Equations with Aftereffect written by N.V. Azbelev and published by CRC Press. This book was released on 2002-10-03 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stability of Differential Equations with Aftereffect presents stability theory for differential equations concentrating on functional differential equations with delay, integro-differential equations, and related topics. The authors provide background material on the modern theory of functional differential equations and introduce some new flexible methods for investigating the asymptotic behaviour of solutions to a range of equations. The treatment also includes some results from the authors' research group based at Perm and provides a useful reference text for graduates and researchers working in mathematical and engineering science.
Author : R. B. White
Publisher : World Scientific
ISBN 13 : 1848166079
Total Pages : 430 pages
Book Rating : 4.8/5 (481 download)
Download or read book Asymptotic Analysis of Differential Equations written by R. B. White and published by World Scientific. This book was released on 2010 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.
Author : Nguyen Van Minh
Publisher :
ISBN 13 : 9781604564563
Total Pages : 0 pages
Book Rating : 4.5/5 (645 download)
Download or read book Lectures on the Asymptotic Behavior of Solutions of Differential Equations written by Nguyen Van Minh and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is composed of lecture notes on courses to graduate students at various universities on the asymptotic behaviour of differential equations. Anyone who has some acquaintance with differential equations in Banach spaces and Functional Analysis can read this book. It is primarily intended for graduate students and beginning researchers in the theory of evolution equations.
Author : Lamberto Cesari
Publisher : Springer Science & Business Media
ISBN 13 : 3642856713
Total Pages : 282 pages
Book Rating : 4.6/5 (428 download)
Download or read book Asymptotic Behavior and Stability Problems in Ordinary Differential Equations written by Lamberto Cesari and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last few decades the theory of ordinary differential equations has grown rapidly under the action of forces which have been working both from within and without: from within, as a development and deepen ing of the concepts and of the topological and analytical methods brought about by LYAPUNOV, POINCARE, BENDIXSON, and a few others at the turn of the century; from without, in the wake of the technological development, particularly in communications, servomechanisms, auto matic controls, and electronics. The early research of the authors just mentioned lay in challenging problems of astronomy, but the line of thought thus produced found the most impressive applications in the new fields. The body of research now accumulated is overwhelming, and many books and reports have appeared on one or another of the multiple aspects of the new line of research which some authors call" qualitative theory of differential equations". The purpose of the present volume is to present many of the view points and questions in a readable short report for which completeness is not claimed. The bibliographical notes in each section are intended to be a guide to more detailed expositions and to the original papers. Some traditional topics such as the Sturm comparison theory have been omitted. Also excluded were all those papers, dealing with special differential equations motivated by and intended for the applications.
Author : Jack K. Hale
Publisher :
ISBN 13 :
Total Pages : 43 pages
Book Rating : 4.:/5 (227 download)
Download or read book Asymptotic Behaviour of Neutral Functional Differential Equations written by Jack K. Hale and published by . This book was released on 1968 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: A functional differential equation of neutral type is an equation for a function x in which the derivative x dot of x at time t depends not only upon the past and present values of x, but also upon the past and present values of x dot. A general class of linear functional differential equations of neutral type is defined in the space of continuous functions. For this class, a variation of constants formula is derived which gives the solution of a nonhomogeneous linear equation with zero initial data as an integral of the forcing function. It is then shown that the kernel in this integral representation can be used to obtain the general solution of the homogeneous equation. The stability properties of the solutions of the homogeneous equation are characterized in terms of the kernel in the variation of constants formula. Section 3 is devoted to the stability of solutions of equations which are linear or nonlinear perturbations of a given linear system. (Author).
Author : M. I. Vishik
Publisher : Cambridge University Press
ISBN 13 : 9780521422376
Total Pages : 172 pages
Book Rating : 4.4/5 (223 download)
Download or read book Asymptotic Behaviour of Solutions of Evolutionary Equations written by M. I. Vishik and published by Cambridge University Press. This book was released on 1992 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: A short but sweet summary of globally asymptotic solutions of evolutionary equations.
Author : O. A. Oleĭnik
Publisher : Cambridge University Press
ISBN 13 : 9780521485371
Total Pages : 218 pages
Book Rating : 4.4/5 (853 download)
Download or read book Some Asymptotic Problems in the Theory of Partial Differential Equations written by O. A. Oleĭnik and published by Cambridge University Press. This book was released on 1996-03-21 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1993, Professor Oleinik was invited to give a series of lectures about her work in the area of partial differential equations. This book contains those lectures, and more.
