Asymptotic Stability for a Class of Functional Differential Equations of Neutral Type PDF Download

Author: Fu-Shiang Peter Tsen
Publisher:
ISBN:
Category :
Languages : en
Pages : 144

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Author: J. K. Hale
Publisher:
ISBN:
Category :
Languages : en
Pages : 15

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Author: Ivanka Stamova
Publisher: Walter de Gruyter
ISBN: 3110221829
Category : Mathematics
Languages : en
Pages : 241

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Book Description
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.

Author: N.V. Azbelev
Publisher: CRC Press
ISBN: 9780415269575
Category : Mathematics
Languages : en
Pages : 246

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Book Description
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.

Author: Richard C. MacCamy
Publisher:
ISBN:
Category : Functional differential equations
Languages : en
Pages : 92

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Author: Leonid Berezansky
Publisher: CRC Press
ISBN: 1000048551
Category : Mathematics
Languages : en
Pages : 615

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Book Description
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: Michael I. Gil'
Publisher: Springer
ISBN: 9462390916
Category : Mathematics
Languages : en
Pages : 311

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Book Description
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.

Author: Jack K. Hale
Publisher: Amer Mathematical Society
ISBN: 9780821839539
Category : Mathematics
Languages : en
Pages : 65

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Author:
Publisher: Elsevier
ISBN: 0080963145
Category : Mathematics
Languages : en
Pages : 233

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Book Description
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.

Author: Alan Richard Hausrath
Publisher:
ISBN:
Category :
Languages : en
Pages : 170

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