Differential Inclusions In A Banach Space

Author : Alexander Tolstonogov
Publisher : Unknown
Page : 320 pages
File Size : 55,8 Mb
Release : 2000-10-31
Category : Electronic
ISBN : 9401594910

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Differential Inclusions in a Banach Space by Alexander Tolstonogov Pdf

This monograph is devoted to the development of a unified approach for studying differential inclusions in a Banach space with non-convex right-hand side, a new branch of the classical theory of ordinary differential equations. Differential inclusions are now a mature field of mathematical activity, with their own methods, techniques, and applications, which range from economics to physics and biology. The current approach relies on ideas and methods from modern functional analysis, general topology, the theory of multifunctions, and continuous selectors. Audience: This volume will be of interest to researchers and postgraduate student whose work involves differential equations, functional analysis, topology, and the theory of set-valued functions.

Author : Alexander Tolstonogov
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 46,5 Mb
Release : 2000-10-31
Category : Mathematics
ISBN : 0792366182

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Differential Inclusions in a Banach Space by Alexander Tolstonogov Pdf

Preface to the English Edition The present monograph is a revised and enlarged alternative of the author's monograph [19] which was devoted to the development of a unified approach to studying differential inclusions, whose values of the right hand sides are compact, not necessarily convex subsets of a Banach space. This approach relies on ideas and methods of modem functional analysis, general topology, the theory of multi-valued mappings and continuous selectors. Although the basic content of the previous monograph has been remained the same this monograph has been partly re-organized and the author's recent results have been added. The contents of the present book are divided into five Chapters and an Appendix. The first Chapter of the J>ook has been left without changes and deals with multi-valued differential equations generated by a differential inclusion. The second Chapter has been significantly revised and extended. Here the au thor's recent results concerning extreme continuous selectors of multi-functions with decomposable values, multi-valued selectors ofmulti-functions generated by a differential inclusion, the existence of solutions of a differential inclusion, whose right hand side has different properties of semicontinuity at different points, have been included. Some of these results made it possible to simplify schemes for proofs concerning the existence of solutions of differential inclu sions with semicontinuous right hand side a.nd to obtain new results. In this Chapter the existence of solutions of different types are considered.

Author : Mikhail I. Kamenskii,Valeri V. Obukhovskii,Pietro Zecca
Publisher : Walter de Gruyter
Page : 245 pages
File Size : 47,8 Mb
Release : 2011-07-20
Category : Mathematics
ISBN : 9783110870893

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Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces by Mikhail I. Kamenskii,Valeri V. Obukhovskii,Pietro Zecca Pdf

The theory of set-valued maps and of differential inclusion is developed in recent years both as a field of his own and as an approach to control theory. The book deals with the theory of semilinear differential inclusions in infinite dimensional spaces. In this setting, problems of interest to applications do not suppose neither convexity of the map or compactness of the multi-operators. These assumption implies the development of the theory of measure of noncompactness and the construction of a degree theory for condensing mapping. Of particular interest is the approach to the case when the linear part is a generator of a condensing, strongly continuous semigroup. In this context, the existence of solutions for the Cauchy and periodic problems are proved as well as the topological properties of the solution sets. Examples of applications to the control of transmission line and to hybrid systems are presented.

Author : Alexander Tolstonogov
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401594905

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Differential Inclusions in a Banach Space by Alexander Tolstonogov Pdf

Preface to the English Edition The present monograph is a revised and enlarged alternative of the author's monograph [19] which was devoted to the development of a unified approach to studying differential inclusions, whose values of the right hand sides are compact, not necessarily convex subsets of a Banach space. This approach relies on ideas and methods of modem functional analysis, general topology, the theory of multi-valued mappings and continuous selectors. Although the basic content of the previous monograph has been remained the same this monograph has been partly re-organized and the author's recent results have been added. The contents of the present book are divided into five Chapters and an Appendix. The first Chapter of the J>ook has been left without changes and deals with multi-valued differential equations generated by a differential inclusion. The second Chapter has been significantly revised and extended. Here the au thor's recent results concerning extreme continuous selectors of multi-functions with decomposable values, multi-valued selectors ofmulti-functions generated by a differential inclusion, the existence of solutions of a differential inclusion, whose right hand side has different properties of semicontinuity at different points, have been included. Some of these results made it possible to simplify schemes for proofs concerning the existence of solutions of differential inclu sions with semicontinuous right hand side a.nd to obtain new results. In this Chapter the existence of solutions of different types are considered.

Author : Andrzej Granas,Marlène Frigon
Publisher : Springer Science & Business Media
Page : 531 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401103398

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Topological Methods in Differential Equations and Inclusions by Andrzej Granas,Marlène Frigon Pdf

The papers collected in this volume are contributions to the 33rd session of the Seminaire de Mathematiques Superieures (SMS) on "Topological Methods in Differential Equations and Inclusions". This session of the SMS took place at the Universite de Montreal in July 1994 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together a considerable group of young researchers from various parts of the world and to present to them coherent surveys of some of the most recent advances in this area of Nonlinear Analysis. During the meeting 89 mathematicians from 20 countries have had the opportunity to get acquainted with various aspects of the subjects treated in the lectures as well as the chance to exchange ideas and learn about new problems arising in the field. The main topics teated in this ASI were the following: Fixed point theory for single- and multi-valued mappings including topological degree and its generalizations, and topological transversality theory; existence and multiplicity results for ordinary differential equations and inclusions; bifurcation and stability problems; ordinary differential equations in Banach spaces; second order differential equations on manifolds; the topological structure of the solution set of differential inclusions; effects of delay perturbations on dynamics of retarded delay differential equations; dynamics of reaction diffusion equations; non smooth critical point theory and applications to boundary value problems for quasilinear elliptic equations.

Author : Smaïl Djebali,Lech Górniewicz,Abdelghani Ouahab
Publisher : Walter de Gruyter
Page : 474 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783110293562

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Solution Sets for Differential Equations and Inclusions by Smaïl Djebali,Lech Górniewicz,Abdelghani Ouahab Pdf

This monograph gives a systematic presentation of classical and recent results obtained in the last couple of years. It comprehensively describes the methods concerning the topological structure of fixed point sets and solution sets for differential equations and inclusions. Many of the basic techniques and results recently developed about this theory are presented, as well as the literature that is disseminated and scattered in several papers of pioneering researchers who developed the functional analytic framework of this field over the past few decades. Several examples of applications relating to initial and boundary value problems are discussed in detail. The book is intended to advanced graduate researchers and instructors active in research areas with interests in topological properties of fixed point mappings and applications; it also aims to provide students with the necessary understanding of the subject with no deep background material needed. This monograph fills the vacuum in the literature regarding the topological structure of fixed point sets and its applications.

Author : Zhengzhi Han,Xiushan Cai,Jun Huang
Publisher : Springer
Page : 344 pages
File Size : 50,6 Mb
Release : 2016-06-15
Category : Technology & Engineering
ISBN : 9783662492451

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Theory of Control Systems Described by Differential Inclusions by Zhengzhi Han,Xiushan Cai,Jun Huang Pdf

This book provides a brief introduction to the theory of finite dimensional differential inclusions, and deals in depth with control of three kinds of differential inclusion systems. The authors introduce the algebraic decomposition of convex processes, the stabilization of polytopic systems, and observations of Luré systems. They also introduce the elemental theory of finite dimensional differential inclusions, and the properties and designs of the control systems described by differential inclusions. Addressing the material with clarity and simplicity, the book includes recent research achievements and spans all concepts, concluding with a critical mathematical framework. This book is intended for researchers, teachers and postgraduate students in the area of automatic control engineering.

Author : J.-P. Aubin,A. Cellina
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 53,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642695124

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Differential Inclusions by J.-P. Aubin,A. Cellina Pdf

A great impetus to study differential inclusions came from the development of Control Theory, i.e. of dynamical systems x'(t) = f(t, x(t), u(t)), x(O)=xo "controlled" by parameters u(t) (the "controls"). Indeed, if we introduce the set-valued map F(t, x)= {f(t, x, u)}ueu then solutions to the differential equations (*) are solutions to the "differen tial inclusion" (**) x'(t)EF(t, x(t)), x(O)=xo in which the controls do not appear explicitely. Systems Theory provides dynamical systems of the form d x'(t)=A(x(t)) dt (B(x(t))+ C(x(t)); x(O)=xo in which the velocity of the state of the system depends not only upon the x(t) of the system at time t, but also on variations of observations state B(x(t)) of the state. This is a particular case of an implicit differential equation f(t, x(t), x'(t)) = 0 which can be regarded as a differential inclusion (**), where the right-hand side F is defined by F(t, x)= {vlf(t, x, v)=O}. During the 60's and 70's, a special class of differential inclusions was thoroughly investigated: those of the form X'(t)E - A(x(t)), x (0) =xo where A is a "maximal monotone" map. This class of inclusions contains the class of "gradient inclusions" which generalize the usual gradient equations x'(t) = -VV(x(t)), x(O)=xo when V is a differentiable "potential". 2 Introduction There are many instances when potential functions are not differentiable

Author : John R. Graef,Johnny Henderson,Abdelghani Ouahab
Publisher : CRC Press
Page : 430 pages
File Size : 40,6 Mb
Release : 2018-09-25
Category : Mathematics
ISBN : 9780429822612

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Topological Methods for Differential Equations and Inclusions by John R. Graef,Johnny Henderson,Abdelghani Ouahab Pdf

Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis.

Author : John R. Graef,Johnny Henderson,Abdelghani Ouahab
Publisher : Walter de Gruyter
Page : 412 pages
File Size : 52,6 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 : Valeri Obukhovskii,Boris Gel'man
Publisher : World Scientific
Page : 221 pages
File Size : 45,8 Mb
Release : 2020-04-04
Category : Mathematics
ISBN : 9789811220234

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Multivalued Maps And Differential Inclusions: Elements Of Theory And Applications by Valeri Obukhovskii,Boris Gel'man Pdf

The theory of multivalued maps and the theory of differential inclusions are closely connected and intensively developing branches of contemporary mathematics. They have effective and interesting applications in control theory, optimization, calculus of variations, non-smooth and convex analysis, game theory, mathematical economics and in other fields.This book presents a user-friendly and self-contained introduction to both subjects. It is aimed at 'beginners', starting with students of senior courses. The book will be useful both for readers whose interests lie in the sphere of pure mathematics, as well as for those who are involved in applicable aspects of the theory. In Chapter 0, basic definitions and fundamental results in topology are collected. Chapter 1 begins with examples showing how naturally the idea of a multivalued map arises in diverse areas of mathematics, continues with the description of a variety of properties of multivalued maps and finishes with measurable multivalued functions. Chapter 2 is devoted to the theory of fixed points of multivalued maps. The whole of Chapter 3 focuses on the study of differential inclusions and their applications in control theory. The subject of last Chapter 4 is the applications in dynamical systems, game theory, and mathematical economics.The book is completed with the bibliographic commentaries and additions containing the exposition related both to the sections described in the book and to those which left outside its framework. The extensive bibliography (including more than 400 items) leads from basic works to recent studies.

Author : Mouffak Benchohra
Publisher : Hindawi Publishing Corporation
Page : 381 pages
File Size : 44,7 Mb
Release : 2006
Category : Differential equations
ISBN : 9789775945501

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Impulsive Differential Equations and Inclusions by Mouffak Benchohra Pdf

Author : Michal Kisielewicz
Publisher : Springer
Page : 268 pages
File Size : 43,8 Mb
Release : 1991-06-30
Category : Language Arts & Disciplines
ISBN : UOM:39015021994937

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Differential Inclusions and Optimal Control by Michal Kisielewicz Pdf

Author : Saïd Abbas,Mouffak Benchohra
Publisher : Springer
Page : 408 pages
File Size : 49,9 Mb
Release : 2015-06-30
Category : Mathematics
ISBN : 9783319177687

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Advanced Functional Evolution Equations and Inclusions by Saïd Abbas,Mouffak Benchohra Pdf

This book presents up-to-date results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and non-densely defined functional differential equations and inclusions in separable Banach spaces or in Fréchet spaces. The tools used include classical fixed points theorems and the measure-of non-compactness, and each chapter concludes with a section devoted to notes and bibliographical remarks. This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.

Author : Lionel Thibault
Publisher : World Scientific
Page : 1629 pages
File Size : 40,9 Mb
Release : 2023-02-14
Category : Mathematics
ISBN : 9789811258183

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Unilateral Variational Analysis In Banach Spaces (In 2 Parts) by Lionel Thibault Pdf

The monograph provides a detailed and comprehensive presentation of the rich and beautiful theory of unilateral variational analysis in infinite dimensions. It is divided into two volumes named Part I and Part II. Starting with the convergence of sets and the semilimits and semicontinuities of multimappings, the first volume develops the theories of tangent cones, of subdifferentials, of convexity and duality in locally convex spaces, of extended mean value inequalities in absence of differentiability, of metric regularity, of constrained optimization problems.The second volume is devoted to special classes of non-smooth functions and sets. It expands the theory of subsmooth functions and sets, of semiconvex functions and multimappings, of primal lower regular functions, of singularities of non-smooth mappings, of prox-regular functions and sets in general spaces, of differentiability of projection mapping and others for prox-regular sets. Both volumes I and II contain, for each chapter, extensive comments covering related developments and historical comments.Connected area fields of the material are: optimization, optimal control, variational inequalities, differential inclusions, mechanics, economics. The book is intended for PhD students, researchers, and practitioners using unilateral variational analysis tools.