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Asymptotic Integration And Stability

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Asymptotic Integration And Stability For Ordinary Functional And Discrete Differential Equations Of Fractional Order

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Author : Baleanu Dumitru
language : en
Publisher: World Scientific
Release Date : 2015-01-15

Asymptotic Integration And Stability For Ordinary Functional And Discrete Differential Equations Of Fractional Order written by Baleanu Dumitru and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-15 with Mathematics categories.

This volume presents several important and recent contributions to the emerging field of fractional differential equations in a self-contained manner. It deals with new results on existence, uniqueness and multiplicity, smoothness, asymptotic development, and stability of solutions. The new topics in the field of fractional calculus include also the Mittag-Leffler and Razumikhin stability, stability of a class of discrete fractional non-autonomous systems, asymptotic integration with a priori given coefficients, intervals of disconjugacy (non-oscillation), existence of Lp solutions for various linear, and nonlinear fractional differential equations.

Asymptotic Integration And Stability

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Author : Dumitru Baleanu
language : en
Publisher: Series on Complexity, Nonlinearity, and Chaos
Release Date : 2015

Asymptotic Integration And Stability written by Dumitru Baleanu and has been published by Series on Complexity, Nonlinearity, and Chaos this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Fractional calculus categories.

Some Stability And Perturbation Problems For Differential And Integral Equations

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Author : Fred Brauer
language : en
Publisher:
Release Date : 1976

Some Stability And Perturbation Problems For Differential And Integral Equations written by Fred Brauer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Differential equations categories.

Asymptotic Behavior And Stability Problems In Ordinary Differential Equations

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Author : Lamberto Cesari
language : en
Publisher: Springer
Release Date : 2013-11-09

Asymptotic Behavior And Stability Problems In Ordinary Differential Equations written by Lamberto Cesari and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-09 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.

Stability And Asymptotic Behavior Of Differential Equations

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Author : W. A. Coppel
language : en
Publisher:
Release Date : 1965

Stability And Asymptotic Behavior Of Differential Equations written by W. A. Coppel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Differential equations categories.

Oscillation Nonoscillation Stability And Asymptotic Properties For Second And Higher Order Functional Differential Equations

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Author : Leonid Berezansky
language : en
Publisher: CRC Press
Release Date : 2020-05-18

Oscillation Nonoscillation Stability And Asymptotic Properties For Second And Higher Order Functional Differential Equations written by Leonid Berezansky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-18 with Mathematics categories.

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.

Stability Theory Of Differential Equations

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Author : Richard Bellman
language : en
Publisher: Courier Corporation
Release Date : 2013-02-20

Stability Theory Of Differential Equations written by Richard Bellman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-20 with Mathematics categories.

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.

Asymptotic Stability Of Steady Compressible Fluids

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Author : Mariarosaria Padula
language : en
Publisher: Springer
Release Date : 2011-07-30

Asymptotic Stability Of Steady Compressible Fluids written by Mariarosaria Padula and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-30 with Mathematics categories.

This volume introduces a systematic approach to the solution of some mathematical problems that arise in the study of the hyperbolic-parabolic systems of equations that govern the motions of thermodynamic fluids. It is intended for a wide audience of theoretical and applied mathematicians with an interest in compressible flow, capillarity theory, and control theory. The focus is particularly on recent results concerning nonlinear asymptotic stability, which are independent of assumptions about the smallness of the initial data. Of particular interest is the loss of control that sometimes results when steady flows of compressible fluids are upset by large disturbances. The main ideas are illustrated in the context of three different physical problems: (i) A barotropic viscous gas in a fixed domain with compact boundary. The domain may be either an exterior domain or a bounded domain, and the boundary may be either impermeable or porous. (ii) An isothermal viscous gas in a domain with free boundaries. (iii) A heat-conducting, viscous polytropic gas.

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 Integration Of Differential And Difference Equations

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Author : Sigrun Bodine
language : en
Publisher: Springer
Release Date : 2015-05-26

Asymptotic Integration Of Differential And Difference Equations written by Sigrun Bodine and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-26 with Mathematics categories.

This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers in asymptotic integration as well to non-experts who are interested in the asymptotic analysis of linear differential and difference equations. It will additionally be of interest to students in mathematics, applied sciences, and engineering. Linear algebra and some basic concepts from advanced calculus are prerequisites.

Asymptotic Integration And Stability

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