Asymptotic Properties Of Solutions Of Systems Of Nonlinear Nonautonomous Ordinary Differential Equations
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Author |
: Ivan Kiguradze |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 343 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9789401118088 |
ISBN-13 |
: 9401118086 |
Rating |
: 4/5 (88 Downloads) |
Synopsis Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations by : Ivan Kiguradze
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.
Author |
: Džumal'din D. Mirzov |
Publisher |
: |
Total Pages |
: 177 |
Release |
: 2004 |
ISBN-10 |
: 8021034297 |
ISBN-13 |
: 9788021034297 |
Rating |
: 4/5 (97 Downloads) |
Synopsis Asymptotic Properties of Solutions of Systems of Nonlinear Nonautonomous Ordinary Differential Equations by : Džumal'din D. Mirzov
Author |
: G. Sansone |
Publisher |
: Elsevier |
Total Pages |
: 553 |
Release |
: 2016-06-06 |
ISBN-10 |
: 9781483135960 |
ISBN-13 |
: 1483135969 |
Rating |
: 4/5 (60 Downloads) |
Synopsis Non-Linear Differential Equations by : G. Sansone
International Series of Monographs in Pure and Applied Mathematics, Volume 67: Non-Linear Differential Equations, Revised Edition focuses on the analysis of the phase portrait of two-dimensional autonomous systems; qualitative methods used in finding periodic solutions in periodic systems; and study of asymptotic properties. The book first discusses general theorems about solutions of differential systems. Periodic solutions, autonomous systems, and integral curves are explained. The text explains the singularities of Briot-Bouquet theory. The selection takes a look at plane autonomous systems. Topics include limiting sets, plane cycles, isolated singular points, index, and the torus as phase space. The text also examines autonomous plane systems with perturbations and autonomous and non-autonomous systems with one degree of freedom. The book also tackles linear systems. Reducible systems, periodic solutions, and linear periodic systems are considered. The book is a vital source of information for readers interested in applied mathematics.
Author |
: George David Birkhoff |
Publisher |
: |
Total Pages |
: 48 |
Release |
: 1908 |
ISBN-10 |
: STANFORD:36105046451709 |
ISBN-13 |
: |
Rating |
: 4/5 (09 Downloads) |
Synopsis Asymptotic Properties of the Solutions of Ordinary Linear Differential Equations Containing a Parameter with Application to Boundary Value and Expansion Problems by : George David Birkhoff
Author |
: Lamberto Cesari |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 282 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642856716 |
ISBN-13 |
: 3642856713 |
Rating |
: 4/5 (16 Downloads) |
Synopsis Asymptotic Behavior and Stability Problems in Ordinary Differential Equations by : Lamberto Cesari
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 |
: Miroslav Bartušek |
Publisher |
: |
Total Pages |
: 104 |
Release |
: 1992 |
ISBN-10 |
: UOM:39015043222085 |
ISBN-13 |
: |
Rating |
: 4/5 (85 Downloads) |
Synopsis Asymptotic Properties of Oscillatory Solutions of Differential Equations of the N-th Order by : Miroslav Bartušek
Author |
: Valery V. Kozlov |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 278 |
Release |
: 2013-01-13 |
ISBN-10 |
: 9783642338175 |
ISBN-13 |
: 3642338178 |
Rating |
: 4/5 (75 Downloads) |
Synopsis Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations by : Valery V. Kozlov
The book is dedicated to the construction of particular solutions of systems of ordinary differential equations in the form of series that are analogous to those used in Lyapunov’s first method. A prominent place is given to asymptotic solutions that tend to an equilibrium position, especially in the strongly nonlinear case, where the existence of such solutions can’t be inferred on the basis of the first approximation alone. The book is illustrated with a large number of concrete examples of systems in which the presence of a particular solution of a certain class is related to special properties of the system’s dynamic behavior. It is a book for students and specialists who work with dynamical systems in the fields of mechanics, mathematics, and theoretical physics.
Author |
: Dimit?r Ba?nov |
Publisher |
: World Scientific |
Total Pages |
: 246 |
Release |
: 1995 |
ISBN-10 |
: 9789810218232 |
ISBN-13 |
: 9810218230 |
Rating |
: 4/5 (32 Downloads) |
Synopsis Impulsive Differential Equations by : Dimit?r Ba?nov
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.
Author |
: |
Publisher |
: Academic Publication |
Total Pages |
: 309 |
Release |
: |
ISBN-10 |
: 9789542940098 |
ISBN-13 |
: 9542940092 |
Rating |
: 4/5 (98 Downloads) |
Synopsis Specific Asymptotic Properties of the Solutions of Impulsive Differential Equations. Methods and Applications by :
Author |
: Nikolaĭ Nikolaevich Bogoli︠u︡bov |
Publisher |
: CRC Press |
Total Pages |
: 556 |
Release |
: 1961 |
ISBN-10 |
: 0677200501 |
ISBN-13 |
: 9780677200507 |
Rating |
: 4/5 (01 Downloads) |
Synopsis Asymptotic Methods in the Theory of Non-linear Oscillations by : Nikolaĭ Nikolaevich Bogoli︠u︡bov