Stability And Asymptotic Behavior Of Differential Equations
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Author |
: W. A. Coppel |
Publisher |
: |
Total Pages |
: 184 |
Release |
: 1965 |
ISBN-10 |
: STANFORD:36105031262939 |
ISBN-13 |
: |
Rating |
: 4/5 (39 Downloads) |
Synopsis Stability and Asymptotic Behavior of Differential Equations by : W. A. Coppel
Author |
: Lamberto Cesari |
Publisher |
: Springer |
Total Pages |
: 278 |
Release |
: 2013-11-09 |
ISBN-10 |
: 9783662403686 |
ISBN-13 |
: 3662403684 |
Rating |
: 4/5 (86 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 |
: Richard Bellman |
Publisher |
: Courier Corporation |
Total Pages |
: 178 |
Release |
: 2013-02-20 |
ISBN-10 |
: 9780486150130 |
ISBN-13 |
: 0486150135 |
Rating |
: 4/5 (30 Downloads) |
Synopsis Stability Theory of Differential Equations by : Richard Bellman
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.
Author |
: Matthaeus Merian |
Publisher |
: |
Total Pages |
: |
Release |
: 1963 |
ISBN-10 |
: OCLC:219552817 |
ISBN-13 |
: |
Rating |
: 4/5 (17 Downloads) |
Synopsis Asymptotic Behavior and Stability Problems in Ordinary Differential Equations by : Matthaeus Merian
Author |
: Thomas Guy Hallam |
Publisher |
: |
Total Pages |
: 126 |
Release |
: 1965 |
ISBN-10 |
: OCLC:9610150 |
ISBN-13 |
: |
Rating |
: 4/5 (50 Downloads) |
Synopsis Asymptotic Behavior and Stability Problems in Ordinary Differential Equations by : Thomas Guy Hallam
Author |
: Victor A. Galaktionov |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 388 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461220503 |
ISBN-13 |
: 1461220505 |
Rating |
: 4/5 (03 Downloads) |
Synopsis A Stability Technique for Evolution Partial Differential Equations by : Victor A. Galaktionov
* 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.
Author |
: Richard Bellman |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 99 |
Release |
: 1959 |
ISBN-10 |
: 9780821812358 |
ISBN-13 |
: 0821812351 |
Rating |
: 4/5 (58 Downloads) |
Synopsis Asymptotic Behavior of Solutions of Differential-Difference Equations by : Richard Bellman
Author |
: Leonid Berezansky |
Publisher |
: CRC Press |
Total Pages |
: 488 |
Release |
: 2020-05-18 |
ISBN-10 |
: 9781000048636 |
ISBN-13 |
: 1000048632 |
Rating |
: 4/5 (36 Downloads) |
Synopsis Oscillation, Nonoscillation, Stability and Asymptotic Properties for Second and Higher Order Functional Differential Equations by : Leonid Berezansky
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 |
: Richard Bellman |
Publisher |
: |
Total Pages |
: 168 |
Release |
: 1949 |
ISBN-10 |
: STANFORD:36105030759638 |
ISBN-13 |
: |
Rating |
: 4/5 (38 Downloads) |
Synopsis A Survey of the Theory of the Boundedness, Stability, and Asymptotic Behavior of Solutions of Linear and Non-linear Differential and Difference Equations by : Richard Bellman
Author |
: Lamberto Cesari |
Publisher |
: |
Total Pages |
: 271 |
Release |
: 1959 |
ISBN-10 |
: OCLC:872413433 |
ISBN-13 |
: |
Rating |
: 4/5 (33 Downloads) |
Synopsis Asymptotic behavior and stability problems in ordinary differential equations by : Lamberto Cesari