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Book Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations

Download or read book Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations written by Ivan Kiguradze and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive review of the developments which have taken place during the last thirty years concerning the asymptotic properties of solutions of nonautonomous ordinary differential equations. The conditions of oscillation of solutions are established, and some general theorems on the classification of equations according to their oscillatory properties are proved. In addition, the conditions are found under which nonlinear equations do not have singular, proper, oscillatory and monotone solutions. The book has five chapters: Chapter I deals with linear differential equations; Chapter II with quasilinear equations; Chapter III with general nonlinear differential equations; and Chapter IV and V deal, respectively, with higher-order and second-order differential equations of the Emden-Fowler type. Each section contains problems, including some which presently remain unsolved. The volume concludes with an extensive list of references. For researchers and graduate students interested in the qualitative theory of differential equations.

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

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.

Book Impulsive Differential Equations

Download or read book Impulsive Differential Equations written by Dimit?r Ba?nov and published by World Scientific. This book was released on 1995 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: The question of the presence of various asymptotic properties of the solutions of ordinary differential equations arises when solving various practical problems. The investigation of these questions is still more important for impulsive differential equations which have a wider field of application than the ordinary ones.The results obtained by treating the asymptotic properties of the solutions of impulsive differential equations can be found in numerous separate articles. The systematized exposition of these results in a separate book will satisfy the growing interest in the problems related to the asymptotic properties of the solutions of impulsive differential equations and their applications.

Book Asymptotic Analysis Of Differential Equations Revised Edition

Download or read book Asymptotic Analysis Of Differential Equations Revised Edition written by White Roscoe B and published by World Scientific. This book was released on 2010-08-16 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives the practical means of finding asymptotic solutions to differential equations, and relates WKB methods, integral solutions, Kruskal-Newton diagrams, and boundary layer theory to one another. The construction of integral solutions and analytic continuation are used in conjunction with the asymptotic analysis, to show the interrelatedness of these methods. Some of the functions of classical analysis are used as examples, to provide an introduction to their analytic and asymptotic properties, and to give derivations of some of the important identities satisfied by them. The emphasis is on the various techniques of analysis: obtaining asymptotic limits, connecting different asymptotic solutions, and obtaining integral representation.

Book Oscillation Theory for Neutral Differential Equations with Delay

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.

Book Asymptotic Properties of the Solutions of Ordinary Linear Differential Equations Containing a Parameter with Application to Boundary Value and Expansion Problems

Download or read book Asymptotic Properties of the Solutions of Ordinary Linear Differential Equations Containing a Parameter with Application to Boundary Value and Expansion Problems written by George David Birkhoff and published by Sagwan Press. This book was released on 2015-08-22 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Book Differential Equations And Applications To Biology And To Industry Proceedings Of The Claremont International Conference Dedicated To The Memory Of Starvros Busenberg 1941 1993

Download or read book Differential Equations And Applications To Biology And To Industry Proceedings Of The Claremont International Conference Dedicated To The Memory Of Starvros Busenberg 1941 1993 written by Kenneth Cooke and published by World Scientific. This book was released on 1995-12-08 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of Professor Stavros Busenberg of Harvey Mudd College, who contributed so greatly to this field during 25 years prior to his untimely death. It contains about 60 invited papers by leading researchers in the areas of dynamical systems, mathematical studies in ecology, epidemics, and physiology, and industrial mathematics. Anyone interested in these areas will find much of value in these contributions.

Book The Strong Nonlinear Limit point limit circle Problem

Download or read book The Strong Nonlinear Limit point limit circle Problem written by John R Graef and published by World Scientific. This book was released on 2017-10-06 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: The limit-point/limit-circle problem had its beginnings more than 100 years ago with the publication of Hermann Weyl's classic paper in Mathematische Annalen in 1910 on linear differential equations. This concept was extended to second-order nonlinear equations in the late 1970's and later, to higher order nonlinear equations. This monograph traces the development of what is known as the strong nonlinear limit-point and limit-circle properties of solutions. In addition to bringing together all such results into one place, some new directions that the study has taken as well as some open problems for future research are indicated.

Book Oscillations Of Third Order Nonlinear Neutral Differential Equations

Download or read book Oscillations Of Third Order Nonlinear Neutral Differential Equations written by Mohammed Bushra and published by LAP Lambert Academic Publishing. This book was released on 2015-07-15 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of functional differential equations in recent years has attracted the attention of many researchers, in the theory and its applications. The simplest and perhaps most natural type of functional differential equation is a "delay differential equation" .This means an equation expressing some derivative of x at time t in terms of x, the values of the function x at previous times .The importance of the delay differential equations comes from its huge applications for instance, the study of problems connected with combustion in rocket motion, the problem of planning in economics, biological problems, population dynamics, the logistic equation, and population growth and mechanics, nuclear reactors, heat flow, neural networks, microbiology, ecology, and physiology, as well as many other applications .The study of oscillation and asymptotic properties of solutions of neutral differential equations with positive and negative coefficients has attracted a good bit of attention in the last several years .

Book The Nonlinear Limit Point Limit Circle Problem

Download or read book The Nonlinear Limit Point Limit Circle Problem written by Miroslav Bartusek and published by Springer Science & Business Media. This book was released on 2011-06-27 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph traces the evolution of the limit–point/limit–circle problem from its 1910 inception, in a paper by Hermann Weyl, to its modern-day extensions to the asymptotic analysis of nonlinear differential equations. The authors distill the classical theorems in the linear case and carefully map the progress from linear to nonlinear limit–point results. The relationship between the limit–point/limit–circle properties and the boundedness, oscillation, and convergence of solutions is explored, and in the final chapter, the connection between limit–point/limit–circle problems and spectral theory is examined in detail. With over 120 references, many open problems, and illustrative examples, this work will be valuable to graduate students and researchers in differential equations, functional analysis, operator theory, and related fields.

Book Asymptotic Properties of Solutions of Systems of Nonlinear Nonautonomous Ordinary Differential Equations

Download or read book Asymptotic Properties of Solutions of Systems of Nonlinear Nonautonomous Ordinary Differential Equations written by Džumal'din D. Mirzov and published by . This book was released on 2004 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Asymptotic Behavior of Solutions of Differential Difference Equations

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: