Asymptotic Behaviour And Stability Problems In Ordinary Differential Equations
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Asymptotic Behavior And Stability Problems In Ordinary Differential Equations
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Author : Lamberto Cesari
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations written by Lamberto Cesari and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Asymptotic Behaviour And Stability Problems In Ordinary Differential Equations
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Author : Lamberto Cesari
language : en
Publisher:
Release Date : 1971
Asymptotic Behaviour And Stability Problems In Ordinary Differential Equations written by Lamberto Cesari and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with categories.
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations
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Author : Matthaeus Merian
language : en
Publisher:
Release Date : 1963
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations written by Matthaeus Merian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with categories.
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations
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Author : Thomas Guy Hallam
language : en
Publisher:
Release Date : 1965
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations written by Thomas Guy Hallam and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with categories.
Differential Difference Equations
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Author : Bellman
language : en
Publisher: Academic Press
Release Date : 1963-01-01
Differential Difference Equations written by Bellman and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963-01-01 with Mathematics categories.
Differential-Difference Equations
Dichotomies And Stability In Nonautonomous Linear Systems
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Author : Yu. A. Mitropolsky
language : en
Publisher: CRC Press
Release Date : 2002-10-10
Dichotomies And Stability In Nonautonomous Linear Systems written by Yu. A. Mitropolsky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-10-10 with Mathematics categories.
Linear nonautonomous equations arise as mathematical models in mechanics, chemistry, and biology. The investigation of bounded solutions to systems of differential equations involves some important and challenging problems of perturbation theory for invariant toroidal manifolds. This monograph is a detailed study of the application of Lyapunov func
Nonlinear Differential Equations And Dynamical Systems
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Author : Ferdinand Verhulst
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Differential Equations And Dynamical Systems written by Ferdinand Verhulst and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
On the subject of differential equations a great many elementary books have been written. This book bridges the gap between elementary courses and the research literature. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed. Stability theory is developed starting with linearisation methods going back to Lyapunov and Poincaré. The global direct method is then discussed. To obtain more quantitative information the Poincaré-Lindstedt method is introduced to approximate periodic solutions while at the same time proving existence by the implicit function theorem. The method of averaging is introduced as a general approximation-normalisation method. The last four chapters introduce the reader to relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, Hamiltonian systems (recurrence, invariant tori, periodic solutions). The book presents the subject material from both the qualitative and the quantitative point of view. There are many examples to illustrate the theory and the reader should be able to start doing research after studying this book.
Nonlinear Ordinary Differential Equations
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Author : R. Grimshaw
language : en
Publisher: Routledge
Release Date : 2017-10-19
Nonlinear Ordinary Differential Equations written by R. Grimshaw and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
Ordinary differential equations have long been an important area of study because of their wide application in physics, engineering, biology, chemistry, ecology, and economics. Based on a series of lectures given at the Universities of Melbourne and New South Wales in Australia, Nonlinear Ordinary Differential Equations takes the reader from basic elementary notions to the point where the exciting and fascinating developments in the theory of nonlinear differential equations can be understood and appreciated. Each chapter is self-contained, and includes a selection of problems together with some detailed workings within the main text. Nonlinear Ordinary Differential Equations helps develop an understanding of the subtle and sometimes unexpected properties of nonlinear systems and simultaneously introduces practical analytical techniques to analyze nonlinear phenomena. This excellent book gives a structured, systematic, and rigorous development of the basic theory from elementary concepts to a point where readers can utilize ideas in nonlinear differential equations.
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations
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Author : Lamberto Cesari
language : de
Publisher:
Release Date : 1959
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations written by Lamberto Cesari and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959 with categories.
Differential And Integral Inequalities
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Author : Wolfgang Walter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Differential And Integral Inequalities written by Wolfgang Walter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In 1964 the author's mono graph "Differential- und Integral-Un gleichungen," with the subtitle "und ihre Anwendung bei Abschätzungs und Eindeutigkeitsproblemen" was published. The present volume grew out of the response to the demand for an English translation of this book. In the meantime the literature on differential and integral in equalities increased greatly. We have tried to incorporate new results as far as possible. As a matter of fact, the Bibliography has been almost doubled in size. The most substantial additions are in the field of existence theory. In Chapter I we have included the basic theorems on Volterra integral equations in Banach space (covering the case of ordinary differential equations in Banach space). Corresponding theorems on differential inequalities have been added in Chapter II. This was done with a view to the new sections; dealing with the line method, in the chapter on parabolic differential equations. Section 35 contains an exposition of this method in connection with estimation and convergence. An existence theory for the general nonlinear parabolic equation in one space variable based on the line method is given in Section 36. This theory is considered by the author as one of the most significant recent applications of in equality methods. We should mention that an exposition of Krzyzanski's method for solving the Cauchy problem has also been added. The numerous requests that the new edition include a chapter on elliptic differential equations have been satisfied to some extent.