Impulsive Differential Equations With A Small Parameter

Author : Drumi D Bainov,Valery Covachev
Publisher : World Scientific
Page : 282 pages
File Size : 40,8 Mb
Release : 1994-12-16
Category : Mathematics
ISBN : 9789814504010

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Impulsive Differential Equations With A Small Parameter by Drumi D Bainov,Valery Covachev Pdf

This book is devoted to impulsive differential equations with a small parameter. It consists of three chapters. Chapter One serves as an introduction. In Chapter Two, regularly perturbed impulsive differential equations are considered. Modifications of the method of small parameter, the averaging method, and the method of integral manifolds are proposed. In Chapter Three, singularly perturbed differential equations are considered. A modification of the method of boundary functions is proposed, and asymptotic expansions along the powers of the small parameters of the solutions of the initial value problem, the periodic problem, and some boundary value problems are found. Numerous nonstandard applications to the theory of optimal control are made. The application of some other methods to impulsive singularly perturbed equations is illustrated, such as the numerical-analytical method for finding periodic solutions, the method of differential inequalities and the averaging method.The book is written clearly, strictly, and understandably. It is intended for mathematicians, physicists, chemists, biologists and economists, as well as for senior students of these specialities.

Author : Drumi Bainov,Pavel Simeonov
Publisher : Routledge
Page : 146 pages
File Size : 45,9 Mb
Release : 2017-11-01
Category : Mathematics
ISBN : 9781351439091

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Impulsive Differential Equations by Drumi Bainov,Pavel Simeonov Pdf

Impulsive differential equations have been the subject of intense investigation in the last 10-20 years, due to the wide possibilities for their application in numerous fields of science and technology. This new work presents a systematic exposition of the results solving all of the more important problems in this field.

Author : Dimit?r Ba?nov,Val‚ry Covachev
Publisher : World Scientific
Page : 292 pages
File Size : 52,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9810214340

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Impulsive Differential Equations with a Small Parameter by Dimit?r Ba?nov,Val‚ry Covachev Pdf

This book is devoted to impulsive differential equations with a small parameter. It consists of three chapters. Chapter One serves as an introduction. In Chapter Two, regularly perturbed impulsive differential equations are considered. Modifications of the method of small parameter, the averaging method, and the method of integral manifolds are proposed. In Chapter Three, singularly perturbed differential equations are considered. A modification of the method of boundary functions is proposed, and asymptotic expansions along the powers of the small parameters of the solutions of the initial value problem, the periodic problem, and some boundary value problems are found. Numerous nonstandard applications to the theory of optimal control are made. The application of some other methods to impulsive singularly perturbed equations is illustrated, such as the numerical-analytical method for finding periodic solutions, the method of differential inequalities and the averaging method.The book is written clearly, strictly, and understandably. It is intended for mathematicians, physicists, chemists, biologists and economists, as well as for senior students of these specialities.

Author : A M Samoilenko,N A Perestyuk
Publisher : World Scientific
Page : 472 pages
File Size : 47,7 Mb
Release : 1995-08-31
Category : Science
ISBN : 9789814499828

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Impulsive Differential Equations by A M Samoilenko,N A Perestyuk Pdf

Contents:General Description of Impulsive Differential SystemsLinear SystemsStability of SolutionsPeriodic and Almost Periodic Impulsive SystemsIntegral Sets of Impulsive SystemsOptimum Control in Impulsive SystemsAsymptotic Study of Oscillations in Impulsive SystemsA Periodic and Almost Periodic Impulsive SystemsBibliographySubject Index Readership: Researchers in nonlinear science. keywords:Differential Equations with Impulses;Linear Systems;Stability;Periodic and Quasi-Periodic Solutions;Integral Sets;Optimal Control “… lucid … the book … will benefit all who are interested in IDE…” Mathematics Abstracts

Author : V. Lakshmikantham,Dimit?r Ba?nov,Pavel S. Simeonov
Publisher : World Scientific
Page : 296 pages
File Size : 46,8 Mb
Release : 1989
Category : Mathematics
ISBN : 9971509709

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Theory of Impulsive Differential Equations by V. Lakshmikantham,Dimit?r Ba?nov,Pavel S. Simeonov Pdf

Many evolution processes are characterized by the fact that at certain moments of time they experience a change of state abruptly. These processes are subject to short-term perturbations whose duration is negligible in comparison with the duration of the process. Consequently, it is natural to assume that these perturbations act instantaneously, that is, in the form of impulses. It is known, for example, that many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, pharmacokinetics and frequency modulated systems, do exhibit impulsive effects. Thus impulsive differential equations, that is, differential equations involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems.

Author : Drumi D Bainov,Pavel Simeonov
Publisher : World Scientific
Page : 246 pages
File Size : 41,8 Mb
Release : 1995-03-29
Category : Mathematics
ISBN : 9789814501880

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Impulsive Differential Equations: Asymptotic Properties Of The Solutions by Drumi D Bainov,Pavel Simeonov Pdf

The question of the presence of various asymptotic properties of the solutions of ordinary differential equations arises when solving various practical problems. The investigation of these questions is still more important for impulsive differential equations which have a wider field of application than the ordinary ones.The results obtained by treating the asymptotic properties of the solutions of impulsive differential equations can be found in numerous separate articles. The systematized exposition of these results in a separate book will satisfy the growing interest in the problems related to the asymptotic properties of the solutions of impulsive differential equations and their applications.

Author : Mouffak Benchohra
Publisher : Hindawi Publishing Corporation
Page : 381 pages
File Size : 54,5 Mb
Release : 2006
Category : Differential equations
ISBN : 9789775945501

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Impulsive Differential Equations and Inclusions by Mouffak Benchohra Pdf

Author : Bainov, D. D.,Kostadinov, S. I.
Publisher : Unknown
Page : 186 pages
File Size : 54,8 Mb
Release : 1996
Category : Differential equations
ISBN : UOM:39015041545602

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Abstract Impulsive Differential Equations by Bainov, D. D.,Kostadinov, S. I. Pdf

Author : Gani T. Stamov
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 40,6 Mb
Release : 2012-03-09
Category : Mathematics
ISBN : 9783642275456

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Almost Periodic Solutions of Impulsive Differential Equations by Gani T. Stamov Pdf

In the present book a systematic exposition of the results related to almost periodic solutions of impulsive differential equations is given and the potential for their application is illustrated.

Author : Drumi Bainov,Pavel Simeonov
Publisher : Routledge
Page : 238 pages
File Size : 49,6 Mb
Release : 2017-11-01
Category : Mathematics
ISBN : 9781351439107

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Impulsive Differential Equations by Drumi Bainov,Pavel Simeonov Pdf

Impulsive differential equations have been the subject of intense investigation in the last 10-20 years, due to the wide possibilities for their application in numerous fields of science and technology. This new work presents a systematic exposition of the results solving all of the more important problems in this field.

Author : Nikolaĭ Alekseevich Peresti͡uk
Publisher : Walter de Gruyter
Page : 325 pages
File Size : 54,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9783110218169

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Differential Equations with Impulse Effects by Nikolaĭ Alekseevich Peresti͡uk Pdf

This monograph is an introduction to the theory of ordinary differential equations with jump conditions at discrete moments of time. From the contents: Pulse differential equations and inclusions Linear systems with multivalued trajectories Method of averaging in systems with pulse action Averaging of differential inclusions Differential equa

Author : Irena Rachůnková,Jan Tomeček
Publisher : Springer
Page : 190 pages
File Size : 46,8 Mb
Release : 2015-09-29
Category : Mathematics
ISBN : 9789462391277

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State-Dependent Impulses by Irena Rachůnková,Jan Tomeček Pdf

This book offers the reader a new approach to the solvability of boundary value problems with state-dependent impulses and provides recently obtained existence results for state dependent impulsive problems with general linear boundary conditions. It covers fixed-time impulsive boundary value problems both regular and singular and deals with higher order differential equations or with systems that are subject to general linear boundary conditions. We treat state-dependent impulsive boundary value problems, including a new approach giving effective conditions for the solvability of the Dirichlet problem with one state-dependent impulse condition and we show that the depicted approach can be extended to problems with a finite number of state-dependent impulses. We investigate the Sturm–Liouville boundary value problem for a more general right-hand side of a differential equation. Finally, we offer generalizations to higher order differential equations or differential systems subject to general linear boundary conditions.

Author : John R. Graef,Johnny Henderson,Abdelghani Ouahab
Publisher : Walter de Gruyter
Page : 412 pages
File Size : 46,8 Mb
Release : 2013-07-31
Category : Mathematics
ISBN : 9783110295313

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Impulsive Differential Inclusions by John R. Graef,Johnny Henderson,Abdelghani Ouahab Pdf

Differential equations with impulses arise as models of many evolving processes that are subject to abrupt changes, such as shocks, harvesting, and natural disasters. These phenomena involve short-term perturbations from continuous and smooth dynamics, whose duration is negligible in comparison with the duration of an entire evolution. In models involving such perturbations, it is natural to assume these perturbations act instantaneously or in the form of impulses. As a consequence, impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, and so forth. There are also many different studies in biology and medicine for which impulsive differential equations provide good models. During the last 10 years, the authors have been responsible for extensive contributions to the literature on impulsive differential inclusions via fixed point methods. This book is motivated by that research as the authors endeavor to bring under one cover much of those results along with results by other researchers either affecting or affected by the authors' work. The questions of existence and stability of solutions for different classes of initial value problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems. In addition, since differential equations can be viewed as special cases of differential inclusions, significant attention is also given to relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its simpler beginnings as well.

Author : Ivanka Stamova
Publisher : Walter de Gruyter
Page : 241 pages
File Size : 53,5 Mb
Release : 2009-10-16
Category : Mathematics
ISBN : 9783110221824

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Stability Analysis of Impulsive Functional Differential Equations by Ivanka Stamova Pdf

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 : Ivanka Stamova,Gani Stamov
Publisher : Springer
Page : 318 pages
File Size : 53,8 Mb
Release : 2016-05-05
Category : Science
ISBN : 9783319280615

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Applied Impulsive Mathematical Models by Ivanka Stamova,Gani Stamov Pdf

Using the theory of impulsive differential equations, this book focuses on mathematical models which reflect current research in biology, population dynamics, neural networks and economics. The authors provide the basic background from the fundamental theory and give a systematic exposition of recent results related to the qualitative analysis of impulsive mathematical models. Consisting of six chapters, the book presents many applicable techniques, making them available in a single source easily accessible to researchers interested in mathematical models and their applications. Serving as a valuable reference, this text is addressed to a wide audience of professionals, including mathematicians, applied researchers and practitioners.