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Asymptotic Behavior And Stability Problems In Ordinary Differential Equations
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Book Synopsis Asymptotic Behavior and Stability Problems in Ordinary Differential Equations by : Lamberto Cesari
Download or read book Asymptotic Behavior and Stability Problems in Ordinary Differential Equations written by Lamberto Cesari and published by Springer. This book was released on 2013-11-09 with total page 278 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.
Book Synopsis Stability and Asymptotic Behavior of Differential Equations by : W. A. Coppel
Download or read book Stability and Asymptotic Behavior of Differential Equations written by W. A. Coppel and published by . This book was released on 1965 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Behavior of Solutions of Differential-Difference Equations by : Richard Bellman
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:
Book Synopsis Stability Theory of Differential Equations by : Richard Bellman
Download or read book Stability Theory of Differential Equations written by Richard Bellman and published by Courier Corporation. This book was released on 2013-02-20 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies. The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from the beginning. In regard to the stability of nonlinear systems, results of the linear theory are used to drive the results of Poincaré and Liapounoff. Professor Bellman then surveys important results concerning the boundedness, stability, and asymptotic behavior of second-order linear differential equations. The final chapters explore significant nonlinear differential equations whose solutions may be completely described in terms of asymptotic behavior. Only real solutions of real equations are considered, and the treatment emphasizes the behavior of these solutions as the independent variable increases without limit.
Book Synopsis Ordinary Differential Equations by : Wolfgang Walter
Download or read book Ordinary Differential Equations written by Wolfgang Walter and published by Springer Science & Business Media. This book was released on 2013-03-11 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a translation of the 6th edition of Gewöhnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for basic theorems. This unique feature of the book calls for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. It is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed.
Book Synopsis Oscillation, Nonoscillation, Stability and Asymptotic Properties for Second and Higher Order Functional Differential Equations by : Leonid Berezansky
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 Synopsis Asymptotic Behavior of Monodromy by : Carlos Simpson
Download or read book Asymptotic Behavior of Monodromy written by Carlos Simpson and published by Springer. This book was released on 1991 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns the question of how the solution of a system of ODE's varies when the differential equation varies. The goal is to give nonzero asymptotic expansions for the solution in terms of a parameter expressing how some coefficients go to infinity. A particular classof families of equations is considered, where the answer exhibits a new kind of behavior not seen in most work known until now. The techniques include Laplace transform and the method of stationary phase, and a combinatorial technique for estimating the contributions of terms in an infinite series expansion for the solution. Addressed primarily to researchers inalgebraic geometry, ordinary differential equations and complex analysis, the book will also be of interest to applied mathematicians working on asymptotics of singular perturbations and numerical solution of ODE's.
Book Synopsis Mathematical Problems in Biology by : P. van den Driessche
Download or read book Mathematical Problems in Biology written by P. van den Driessche and published by Springer. This book was released on 1974-10-04 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: A conference on "Some Mathematical Problems in Biology" was held at the University of Victoria, Victoria, B. C. , Canada, from May 7 - 10, 1973. The participants and invited speakers were mathematicians interested in problems of a biological nature, and scientists actively engaged in developing mathematical models in biological fields. One aim of the conference was to attempt to assess what the recent rapid growth of mathematical interaction with the biosciences has accomplished and may accomplish in the near future. The conference also aimed to expose the problems of communication bet~",een mathematicians and biological scientists, and in doing so to stimulate the interchange of ideas. It was recognised that the topic spans an enormous breadth, and little attempt was made to balance the very diverse areas. Widespread active interest was shown in the conference, and just over one hundred people registered. The varied departments and institutions across North America from which the participants came made it both academically and geographically mixed. The chief activity of the conference was the presentation of papers. Nine invited guest speakers (see table of contents) each gave a one hour talk. These covered a wide range of topics. There were twenty-five shorter (twenty minute) contributed papers, and almost all papers l,rere followed by a five minute question and discussion period. Duplicated abstracts of presented papers were available at the meeting. An evening informal discussion meeting of participants, chaired by Dr. A. B. Tayler, and led by Drs. E. M. Hagmeier, E. C.
Book Synopsis Asymptotic Behavior of Dissipative Systems by : Jack K. Hale
Download or read book Asymptotic Behavior of Dissipative Systems written by Jack K. Hale and published by American Mathematical Soc.. This book was released on 2010-01-04 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph reports the advances that have been made in the area by the author and many other mathematicians; it is an important source of ideas for the researchers interested in the subject. --Zentralblatt MATH Although advanced, this book is a very good introduction to the subject, and the reading of the abstract part, which is elegant, is pleasant. ... this monograph will be of valuable interest for those who aim to learn in the very rapidly growing subject of infinite-dimensional dissipative dynamical systems. --Mathematical Reviews This book is directed at researchers in nonlinear ordinary and partial differential equations and at those who apply these topics to other fields of science. About one third of the book focuses on the existence and properties of the flow on the global attractor for a discrete or continuous dynamical system. The author presents a detailed discussion of abstract properties and examples of asymptotically smooth maps and semigroups. He also covers some of the continuity properties of the global attractor under perturbation, its capacity and Hausdorff dimension, and the stability of the flow on the global attractor under perturbation. The remainder of the book deals with particular equations occurring in applications and especially emphasizes delay equations, reaction-diffusion equations, and the damped wave equations. In each of the examples presented, the author shows how to verify the existence of a global attractor, and, for several examples, he discusses some properties of the flow on the global attractor.
Author :Victor A. Galaktionov Publisher :Springer Science & Business Media ISBN 13 :1461220505 Total Pages :388 pages Book Rating :4.4/5 (612 download)
Book Synopsis A Stability Technique for Evolution Partial Differential Equations by : Victor A. Galaktionov
Download or read book A Stability Technique for Evolution Partial Differential Equations written by Victor A. Galaktionov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations. * Written by established mathematicians at the forefront of their field, this blend of delicate analysis and broad application is ideal for a course or seminar in asymptotic analysis and nonlinear PDEs. * Well-organized text with detailed index and bibliography, suitable as a course text or reference volume.
Book Synopsis Asymptotic Issues For Some Partial Differential Equations (Second Edition) by : Michel Marie Chipot
Download or read book Asymptotic Issues For Some Partial Differential Equations (Second Edition) written by Michel Marie Chipot and published by World Scientific. This book was released on 2024-04-15 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary focus of the book is to explore the asymptotic behavior of problems formulated within cylindrical structures. Various physical applications are discussed, with certain topics such as fluid flows in channels being particularly noteworthy. Additionally, the book delves into the relevance of elasticity in the context of cylindrical bodies.In specific scenarios where the size of the cylinder becomes exceptionally large, the material's behavior is determined solely by its cross-section. The investigation centers around understanding these particular properties.Since the publication of the first edition, several significant advancements have been made, adding depth and interest to the content. Consequently, new sections have been incorporated into the existing edition, complemented by a comprehensive list of references.
Book Synopsis Topics on Stability and Periodicity in Abstract Differential Equations by :
Download or read book Topics on Stability and Periodicity in Abstract Differential Equations written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Qualitative Theory of Ordinary Differential Equations by : Fred Brauer
Download or read book The Qualitative Theory of Ordinary Differential Equations written by Fred Brauer and published by Courier Corporation. This book was released on 2012-12-11 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Superb, self-contained graduate-level text covers standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters. Focuses on stability theory and its applications to oscillation phenomena, self-excited oscillations, more. Includes exercises.
Book Synopsis International Conference on Differential Equations by : H.A. Antosiewicz
Download or read book International Conference on Differential Equations written by H.A. Antosiewicz and published by Academic Press. This book was released on 2014-05-10 with total page 857 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Conference on Differential Equations contains the proceedings of an International Conference on Differential Equations held at the University of Southern California, on September 3-7, 1974. The papers review advances in the qualitative-analytic theory of differential equations and highlight three broad areas: analytic theory (singular perturbations), qualitative theory (boundary value problems), and mathematical control theory (variational methods). Comprised of 82 chapters, this book begins with a discussion on continuous extensions, their construction, and their application in the theory of differential equations. The reader is then introduced to an approach to boundary control of partial differential equations based on the theory of semigroups of operators; lower closure and existence theorems in optimal control; and a nonlinear oscillation theorem. Subsequent chapters focus on matrices of rational functions; asymptotic integration of linear differential systems; solutions near bifurcated steady states; and geometric views in existence theory. This monograph will be of interest to students and instructors of mathematics.
Book Synopsis Topics on Stability and Periodicity in Abstract Differential Equations by : Gaston M. N'Guerekata
Download or read book Topics on Stability and Periodicity in Abstract Differential Equations written by Gaston M. N'Guerekata and published by World Scientific. This book was released on 2008 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent methods of study on the asymptotic behavior of solutions of abstract differential equations such as stability, exponential dichotomy, periodicity, almost periodicity, and almost automorphy of solutions. The chosen methods are described in a way that is suitable to those who have some experience with ordinary differential equations. The book is intended for graduate students and researchers in the related areas.
Book Synopsis Recent Advances in Differential Equations by : Roberto Conti
Download or read book Recent Advances in Differential Equations written by Roberto Conti and published by Elsevier. This book was released on 2014-05-10 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent Advances in Differential Equations contains the proceedings of a meeting held at the International Center for Theoretical Physics in Trieste, Italy, on August 24-28, 1978 under the auspices of the U.S. Army Research Office. The papers review the status of research in the field of differential equations (ordinary, partial, and functional). Both theoretical aspects (differential operators, periodic solutions, stability and bifurcation, asymptotic behavior of solutions, etc.) and problems arising from applications (reaction-diffusion equations, control problems, heat flow, etc.) are discussed. Comprised of 33 chapters, this book first examines non-cooperative trajectories of n-person dynamical games and stable non-cooperative equilibria, followed by a discussion on the determination and application of Vekua resolvents. The reader is then introduced to generalized Hopf bifurcation; some Cauchy problems arising in computational methods; and boundary value problems for pairs of ordinary differential operators. Subsequent chapters focus on degenerate evolution equations and singular optimal control; stability of neutral functional differential equations; local exact controllability of nonlinear evolution equations; and turbulence and higher order bifurcations. This monograph will be of interest to students and practitioners in the field of mathematics.
Book Synopsis Nonlinear Partial Differential Equations by : Mi-Ho Giga
Download or read book Nonlinear Partial Differential Equations written by Mi-Ho Giga and published by Springer Science & Business Media. This book was released on 2010-05-30 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work will serve as an excellent first course in modern analysis. The main focus is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. This textbook will be an excellent resource for self-study or classroom use.
