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Author : Glenn F. Webb
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (241 download)
Download or read book Asymptotic Stability for Abstract Nonlinear Functional Differential Equations written by Glenn F. Webb and published by . This book was released on 1974* with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : César Ramírez Ibañez
Publisher :
ISBN 13 :
Total Pages : 156 pages
Book Rating : 4.:/5 (973 download)
Download or read book Stability of Nonlinear Functional Differential Equations by the Contraction Mapping Principle written by César Ramírez Ibañez and published by . This book was released on 2016 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fixed point theory has a long history of being used in nonlinear differential equations, in order to prove existence, uniqueness, or other qualitative properties of solutions. However, using the contraction mapping principle for stability and asymptotic stability of solutions is of more recent appearance. Lyapunov functional methods have dominated the determination of stability for general nonlinear systems without solving the systems themselves. In particular, as functional differential equations (FDEs) are more complicated than ODEs, obtaining methods to determine stability of equations that are difficult to handle takes precedence over analytical formulas. Applying Lyapunov techniques can be challenging, and the Banach fixed point method has been shown to yield less restrictive criteria for stability of delayed FDEs. We will study how to apply the contraction mapping principle to stability under different conditions to the ones considered by previous authors. We will first extend a contraction mapping stability result that gives asymptotic stability of a nonlinear time-delayed scalar FDE which is linearly dominated by the last state of the system, in order to obtain uniform stability plus asymptotic stability. We will also generalize to the vector case. Afterwards we do further extension by considering an impulsively perturbed version of the previous result, and subsequently we shall use impulses to stabilize an unstable system, under a contraction method paradigm. At the end we also extend the method to a time dependent switched system, where difficulties that do not arise in non-switched systems show up, namely a dwell-time condition, which has already been studied by previous authors using Lyapunov methods. In this study, we will also deepen understanding of this method, as well as point out some other difficulties about using this technique, even for non-switched systems. The purpose is to prompt further investigations into this method, since sometimes one must consider more than one aspect other than stability, and having more than one stability criterion might yield benefits to the modeler.
Author : Tarō Yoshizawa
Publisher :
ISBN 13 : 9789814539647
Total Pages : 380 pages
Book Rating : 4.5/5 (396 download)
Download or read book Functional Differential Equations written by Tarō Yoshizawa and published by . This book was released on 1991 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard C. MacCamy
Publisher :
ISBN 13 :
Total Pages : 92 pages
Book Rating : 4.:/5 (457 download)
Download or read book Asymptotic Stability for a Class of Functional Differential Equations written by Richard C. MacCamy and published by . This book was released on 1972 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kai Liu
Publisher : Cambridge University Press
ISBN 13 : 1108705170
Total Pages : 277 pages
Book Rating : 4.1/5 (87 download)
Download or read book Stochastic Stability of Differential Equations in Abstract Spaces written by Kai Liu and published by Cambridge University Press. This book was released on 2019-05-02 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a unified treatment of stochastic differential equations in abstract, mainly Hilbert, spaces.
Author : Leonid Berezansky
Publisher : CRC Press
ISBN 13 : 1000048551
Total Pages : 615 pages
Book Rating : 4.0/5 ( download)
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 615 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.
Author : T Yoshizawa
Publisher : World Scientific
ISBN 13 : 9814569542
Total Pages : 394 pages
Book Rating : 4.8/5 (145 download)
Download or read book Functional Differential Equations - Proceedings Of The International Symposium written by T Yoshizawa and published by World Scientific. This book was released on 1991-04-30 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Privacy is an unwieldy concept that has eluded an essentialised definition despite its centrality and importance in the body of bioethics. The compilation presented in this volume represents continuing discussions on the theme of privacy in the context of genetic information. It is intended to present a wide range of expert opinion in which the notion of privacy is examined from many perspectives, in different contexts and imperatives, and in different societies, with the hope of advancing an understanding of privacy through the examination and critique of some of its evolving component concepts such as notions of what constitute the personal, the context of privacy, the significance and impact of the relational interests of others who may share the same genetic inheritance, and mechanisms for the protection of privacy (as well as of their limitations), among others. More specifically, the discussions in this volume encourages us to think broadly about privacy, as encompassing values that are entailed in the sociality of context and of relations, and also as freedom from illegitimate and excessive surveillance. A long-standing question that continues to challenge us is whether genetic information should be regarded as exceptional, as it is often perceived. A conclusion that could be derived from this volume is that while genetic information may be significant, it is not exceptionally so. The work presented in this volume underlines the continuing and growing relevance of notions of privacy to genomic science, and the need to take ownership of a genetic privacy for the future through broad, rigorous and open discussion.Contributors: Alastair V Campbell, Benjamin Capps, Jacqueline JL Chin, Oi Lian Kon, Kenji Matsui, Thomas H Murray, Nazirudin Mohd Nasir, Dianne Nicol, Anh Tuan Nuyen, Onora O'Neill, Margaret Otlowski, Yvette van der Eijk, Chunshui Wang, Ross S White.
Author : Lakshmikantham
Publisher : Academic Press
ISBN 13 : 0080955649
Total Pages : 335 pages
Book Rating : 4.0/5 (89 download)
Download or read book Differential and integral inequalities; theory and applications PART B: Functional, partial, abstract, and complex differential equations written by Lakshmikantham and published by Academic Press. This book was released on 1969 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential and integral inequalities; theory and applications PART B: Functional, partial, abstract, and complex differential equations
Author :
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (98 download)
Download or read book On the Asymptotic Stability of Solutions of Functional Differential Equations written by and published by . This book was released on 1979 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Béla Szőkefalvi-Nagy
Publisher : North Holland
ISBN 13 :
Total Pages : 738 pages
Book Rating : 4.:/5 (318 download)
Download or read book Qualitative Theory of Differential Equations written by Béla Szőkefalvi-Nagy and published by North Holland. This book was released on 1990 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains expounded versions of the lectures given at the recent Colloquium. The papers are mostly devoted to the study of asymptotic properties of (and stability problems relating to) solutions of ordinary and functional differential equations. Also featured is the new approach to nonlinear differential equations, using the methods of abstract dynamical systems. Papers concerned with applications in mechanics, physics, biology, and control, may also be found.
Author : Lamberto Cesari
Publisher : Springer
ISBN 13 : 3662403684
Total Pages : 278 pages
Book Rating : 4.6/5 (624 download)
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.
Author : Fu-Shiang Peter Tsen
Publisher :
ISBN 13 :
Total Pages : 144 pages
Book Rating : 4.:/5 (473 download)
Download or read book Asymptotic Stability for a Class of Functional Differential Equations of Neutral Type written by Fu-Shiang Peter Tsen and published by . This book was released on 1978 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Shuhui Wu
Publisher : GRIN Verlag
ISBN 13 : 3346600963
Total Pages : 193 pages
Book Rating : 4.3/5 (466 download)
Download or read book The Asymptotic and Oscillatory Behaviour of Difference and Differential Equations written by Shuhui Wu and published by GRIN Verlag. This book was released on 2022-03-04 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Doctoral Thesis / Dissertation from the year 2009 in the subject Mathematics - Applied Mathematics, London Metropolitan University, language: English, abstract: This thesis deals with the asymptotic and oscillatory behaviour of the solutions of certain differential and difference equations. It mainly consists of three parts. The first part is to study the asymptotic behaviour of certain differential equations. The second part is to look for oscillatory criteria for certain nonlinear neutral differential equations. And the third part is to establish new criteria for a class of nonlinear neutral difference equations of any order with continuous variable and another type of higher even order nonlinear neutral difference equations to be oscillatory. A functional differential equation is a differential equation involving the values of the unknown functions at present, as well as at past or future time. The word “time” here stands for the independent variable. In the thesis, the concept of a functional differential equation is confined to ordinary differential equations, although it suits partial ones as well. Functional differential equations can be classified into four types according to their deviations: retarded, advanced, neutral and mixed. A neutral equation is one in which derivative of functionals of the past history and the present state are involved, but no future states occur in the equation. The order of a differential equation is the order of the highest derivative of the unknown function. A difference equation is a specific type of recurrence relation, which is an equation that defines a sequence recursively: each term of the sequence is defined as a function of the preceding terms. On the other hand, difference equations can be thought of as the discrete analogue of the corresponding differential equations. By analogy with differential equations, difference equations also can be classified into four types: delay, advanced, neutral, and mixed. The order of a difference equation is the difference between the largest and the smallest values of the integer variable explicitly involved in the difference equation.
Author : T. A. Burton
Publisher : Elsevier
ISBN 13 : 0080958672
Total Pages : 349 pages
Book Rating : 4.0/5 (89 download)
Download or read book Stability and Periodic Solutions of Ordinary and Functional Differential Equations written by T. A. Burton and published by Elsevier. This book was released on 1985-12-19 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering
Author : V. Lakshmikantham
Publisher :
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.3/5 (91 download)
Download or read book Differential and Integral Inequalities: Functional, partial, abstract, and complex differential equations written by V. Lakshmikantham and published by . This book was released on 1969 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. K. Hale
Publisher :
ISBN 13 :
Total Pages : 15 pages
Book Rating : 4.:/5 (227 download)
Download or read book On the Uniform Asymptotic Stability of Functional Differential Equations of the Neutral Type written by J. K. Hale and published by . This book was released on 1970 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jack K. Hale
Publisher : Springer Science & Business Media
ISBN 13 : 146129892X
Total Pages : 374 pages
Book Rating : 4.4/5 (612 download)
Download or read book Theory of Functional Differential Equations written by Jack K. Hale and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of my lecture notes, Functional Differential Equations in the Applied Mathematical Sciences series, many new developments have occurred. As a consequence, it was decided not to make a few corrections and additions for a second edition of those notes, but to present a more compre hensive theory. The present work attempts to consolidate those elements of the theory which have stabilized and also to include recent directions of research. The following chapters were not discussed in my original notes. Chapter 1 is an elementary presentation of linear differential difference equations with constant coefficients of retarded and neutral type. Chapter 4 develops the recent theory of dissipative systems. Chapter 9 is a new chapter on perturbed systems. Chapter 11 is a new presentation incorporating recent results on the existence of periodic solutions of autonomous equations. Chapter 12 is devoted entirely to neutral equations. Chapter 13 gives an introduction to the global and generic theory. There is also an appendix on the location of the zeros of characteristic polynomials. The remainder of the material has been completely revised and updated with the most significant changes occurring in Chapter 3 on the properties of solutions, Chapter 5 on stability, and Chapter lOon behavior near a periodic orbit.
