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Asymptotic Stability For A Class Of Functional Differential Equations Of Neutral Type
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Book Synopsis Asymptotic Stability for a Class of Functional Differential Equations of Neutral Type by : Fu-Shiang Peter Tsen
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:
Book Synopsis On the Uniform Asymptotic Stability of Functional Differential Equations of the Neutral Type by : J. K. Hale
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:
Book Synopsis Stability Analysis of Impulsive Functional Differential Equations by : Ivanka Stamova
Download or read book Stability Analysis of Impulsive Functional Differential Equations written by Ivanka Stamova and published by Walter de Gruyter. This book was released on 2009-10-16 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to impulsive functional differential equations which are a natural generalization of impulsive ordinary differential equations (without delay) and of functional differential equations (without impulses). At the present time the qualitative theory of such equations is under rapid development. After a presentation of the fundamental theory of existence, uniqueness and continuability of solutions, a systematic development of stability theory for that class of problems is given which makes the book unique. It addresses to a wide audience such as mathematicians, applied researches and practitioners.
Book Synopsis Stability of Differential Equations with Aftereffect by : N.V. Azbelev
Download or read book Stability of Differential Equations with Aftereffect written by N.V. Azbelev and published by CRC Press. This book was released on 2002-10-03 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stability of Differential Equations with Aftereffect presents stability theory for differential equations concentrating on functional differential equations with delay, integro-differential equations, and related topics. The authors provide background material on the modern theory of functional differential equations and introduce some new flexible methods for investigating the asymptotic behaviour of solutions to a range of equations. The treatment also includes some results from the authors' research group based at Perm and provides a useful reference text for graduates and researchers working in mathematical and engineering science.
Book Synopsis Asymptotic Stability for a Class of Functional Differential Equations by : Richard C. MacCamy
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:
Book Synopsis Oscillation, Nonoscillation, Stability and Asymptotic Properties for Second and Higher Order Functional Differential Equations by : Leonid Berezansky
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.
Book Synopsis A Class of Functional Equations of Neutral Type by : Jack K. Hale
Download or read book A Class of Functional Equations of Neutral Type written by Jack K. Hale and published by Amer Mathematical Society. This book was released on 2005-08-22 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stability of Neutral Functional Differential Equations by : Michael I. Gil'
Download or read book Stability of Neutral Functional Differential Equations written by Michael I. Gil' and published by Springer. This book was released on 2014-10-08 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph the author presents explicit conditions for the exponential, absolute and input-to-state stabilities including solution estimates of certain types of functional differential equations. The main methodology used is based on a combination of recent norm estimates for matrix-valued functions, comprising the generalized Bohl-Perron principle, together with its integral version and the positivity of fundamental solutions. A significant part of the book is especially devoted to the solution of the generalized Aizerman problem.
Book Synopsis Stability of Functional Differential Equations by :
Download or read book Stability of Functional Differential Equations written by and published by Elsevier. This book was released on 1986-04-15 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the structure and stability properties of solutions of functional differential equations. Numerous examples of applications (such as feedback systrems with aftereffect, two-reflector antennae, nuclear reactors, mathematical models in immunology, viscoelastic bodies, aeroautoelastic phenomena and so on) are considered in detail. The development is illustrated by numerous figures and tables.
Book Synopsis Stability Properties of a Class of Functional Differential Equations of Neutral Type by : Alan Richard Hausrath
Download or read book Stability Properties of a Class of Functional Differential Equations of Neutral Type written by Alan Richard Hausrath and published by . This book was released on 1972 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Behaviour of Neutral Functional Differential Equations by : Jack K. Hale
Download or read book Asymptotic Behaviour of Neutral Functional Differential Equations written by Jack K. Hale and published by . This book was released on 1968 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: A functional differential equation of neutral type is an equation for a function x in which the derivative x dot of x at time t depends not only upon the past and present values of x, but also upon the past and present values of x dot. A general class of linear functional differential equations of neutral type is defined in the space of continuous functions. For this class, a variation of constants formula is derived which gives the solution of a nonhomogeneous linear equation with zero initial data as an integral of the forcing function. It is then shown that the kernel in this integral representation can be used to obtain the general solution of the homogeneous equation. The stability properties of the solutions of the homogeneous equation are characterized in terms of the kernel in the variation of constants formula. Section 3 is devoted to the stability of solutions of equations which are linear or nonlinear perturbations of a given linear system. (Author).
Book Synopsis The Asymptotic and Oscillatory Behaviour of Difference and Differential Equations by : Shuhui Wu
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.
Book Synopsis On the Asymptotic Stability of Solutions of Functional Differential Equations by :
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:
Book Synopsis Stability & Periodic Solutions of Ordinary & Functional Differential Equations by : T. A. Burton
Download or read book Stability & Periodic Solutions of Ordinary & Functional Differential Equations written by T. A. Burton and published by Courier Corporation. This book was released on 2014-06-24 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book's discussion of a broad class of differential equations includes linear differential and integrodifferential equations, fixed-point theory, and the basic stability and periodicity theory for nonlinear ordinary and functional differential equations.
Book Synopsis Asymptotic Stability for Abstract Nonlinear Functional Differential Equations by : Glenn F. Webb
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:
Book Synopsis Stability of Functional Differential Equations of Neutral Type by : Marianito A. Cruz
Download or read book Stability of Functional Differential Equations of Neutral Type written by Marianito A. Cruz and published by . This book was released on 1968 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: A functional differential equation of neutral type is a differential system in which the rate of change of the system depends not only upon the past history but also the derivative of the past history of the system. For example, the system (1.1) x dot (t) + A x dot (t - 1) = f(t, x(t), x(t - 1)) is a functional differential or differential difference equation of neutral type. It is the purpose of this paper to give sufficient conditions for the stability and instability of solutions of a large class of equations (1.1) in terms of functions similar to those occurring in the application of the second method of Liapunov to ordinary and functional differential equations of retarded type. The basic restriction on the class of systems is that the derivatives occur linearly with coefficients depending only upon t and that the 'difference' operator associated with the equation is stable. (Author).
Book Synopsis Asymptotic Behavior and Stability Problems in Ordinary Differential Equations by : Lamberto Cesari
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.
