Solution Sets Of Differential Equations In Abstract Spaces

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Solution Sets Of Differential Equations In Abstract Spaces

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Author : Robert Dragoni
language : en
Publisher: CRC Press
Release Date : 1996-04-03

Solution Sets Of Differential Equations In Abstract Spaces written by Robert Dragoni and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-04-03 with Mathematics categories.

This book presents results on the geometric/topological structure of the solution set S of an initial-value problem x(t) = f(t, x(t)), x(0) =xo, when f is a continuous function with values in an infinite-dimensional space. A comprehensive survey of existence results and the properties of S, e.g. when S is a connected set, a retract, an acyclic set, is presented. The authors also survey results onthe properties of S for initial-value problems involving differential inclusions, and for boundary-value problems. This book will be of particular interest to researchers in ordinary and partial differential equations and some workers in control theory.

Solution Sets Of Differential Equations In Abstract Spaces

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Author : Robert Dragoni
language : en
Publisher: Chapman and Hall/CRC
Release Date : 1996-04-03

Solution Sets Of Differential Equations In Abstract Spaces written by Robert Dragoni and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-04-03 with Mathematics categories.

This book presents results on the geometric/topological structure of the solution set S of an initial-value problem x(t) = f(t, x(t)), x(0) =xo, when f is a continuous function with values in an infinite-dimensional space. A comprehensive survey of existence results and the properties of S, e.g. when S is a connected set, a retract, an acyclic set, is presented. The authors also survey results onthe properties of S for initial-value problems involving differential inclusions, and for boundary-value problems. This book will be of particular interest to researchers in ordinary and partial differential equations and some workers in control theory.

Solution Sets For Differential Equations And Inclusions

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Author : Smaïl Djebali
language : en
Publisher: Walter de Gruyter
Release Date : 2012-12-06

Solution Sets For Differential Equations And Inclusions written by Smaïl Djebali and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Differential Equations In Abstract Spaces

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Author : Lakshmikantham
language : en
Publisher: Academic Press
Release Date : 1972-06-16

Differential Equations In Abstract Spaces written by Lakshmikantham and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-06-16 with Computers categories.

Differential Equations in Abstract Spaces

Generalized Ordinary Differential Equations In Abstract Spaces And Applications

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Author : Everaldo M. Bonotto
language : en
Publisher: John Wiley & Sons
Release Date : 2021-08-26

Generalized Ordinary Differential Equations In Abstract Spaces And Applications written by Everaldo M. Bonotto and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-26 with Mathematics categories.

GENERALIZED ORDINARY DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES AND APPLICATIONS Explore a unified view of differential equations through the use of the generalized ODE from leading academics in mathematics Generalized Ordinary Differential Equations in Abstract Spaces and Applications delivers a comprehensive treatment of new results of the theory of Generalized ODEs in abstract spaces. The book covers applications to other types of differential equations, including Measure Functional Differential Equations (measure FDEs). It presents a uniform collection of qualitative results of Generalized ODEs and offers readers an introduction to several theories, including ordinary differential equations, impulsive differential equations, functional differential equations, dynamical equations on time scales, and more. Throughout the book, the focus is on qualitative theory and on corresponding results for other types of differential equations, as well as the connection between Generalized Ordinary Differential Equations and impulsive differential equations, functional differential equations, measure differential equations and dynamic equations on time scales. The book’s descriptions will be of use in many mathematical contexts, as well as in the social and natural sciences. Readers will also benefit from the inclusion of: A thorough introduction to regulated functions, including their basic properties, equiregulated sets, uniform convergence, and relatively compact sets An exploration of the Kurzweil integral, including its definitions and basic properties A discussion of measure functional differential equations, including impulsive measure FDEs The interrelationship between generalized ODEs and measure FDEs A treatment of the basic properties of generalized ODEs, including the existence and uniqueness of solutions, and prolongation and maximal solutions Perfect for researchers and graduate students in Differential Equations and Dynamical Systems, Generalized Ordinary Differential Equations in Abstract Spaces and Applications will also earn a place in the libraries of advanced undergraduate students taking courses in the subject and hoping to move onto graduate studies.

Topological Structure Of The Solution Set For Evolution Inclusions

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Author : Yong Zhou
language : en
Publisher: Springer
Release Date : 2017-10-31

Topological Structure Of The Solution Set For Evolution Inclusions written by Yong Zhou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-31 with Mathematics categories.

This book systematically presents the topological structure of solution sets and attractability for nonlinear evolution inclusions, together with its relevant applications in control problems and partial differential equations. It provides readers the background material needed to delve deeper into the subject and explore the rich research literature. In addition, the book addresses many of the basic techniques and results recently developed in connection with this theory, including the structure of solution sets for evolution inclusions with m-dissipative operators; quasi-autonomous and non-autonomous evolution inclusions and control systems; evolution inclusions with the Hille-Yosida operator; functional evolution inclusions; impulsive evolution inclusions; and stochastic evolution inclusions. Several applications of evolution inclusions and control systems are also discussed in detail. Based on extensive research work conducted by the authors and other experts over the past four years, the information presented is cutting-edge and comprehensive. As such, the book fills an important gap in the body of literature on the structure of evolution inclusions and its applications.

Nonlinear Differential Equations In Abstract Spaces

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Author : V. Lakshmikantham
language : en
Publisher: Pergamon
Release Date : 1981

Nonlinear Differential Equations In Abstract Spaces written by V. Lakshmikantham and has been published by Pergamon this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.

Many problems in partial differential equations which arise from physical models can be considered as ordinary differential equations in appropriate infinite dimensional spaces, for which elegant theories and powerful techniques have recently been developed. This book gives a detailed account of the current state of the theory of nonlinear differential equations in a Banach space, and discusses existence theory for differential equations with continuous and discontinuous right-hand sides. Of special importance is the first systematic presentation of the very important and complex theory of multivalued discontinuous differential equations

Almost Periodic And Almost Automorphic Functions In Abstract Spaces

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Author : Gaston M. N'Guérékata
language : en
Publisher: Springer Nature
Release Date : 2021-05-28

Almost Periodic And Almost Automorphic Functions In Abstract Spaces written by Gaston M. N'Guérékata and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-28 with Mathematics categories.

This book presents the foundation of the theory of almost automorphic functions in abstract spaces and the theory of almost periodic functions in locally and non-locally convex spaces and their applications in differential equations. Since the publication of Almost automorphic and almost periodic functions in abstract spaces (Kluwer Academic/Plenum, 2001), there has been a surge of interest in the theory of almost automorphic functions and applications to evolution equations. Several generalizations have since been introduced in the literature, including the study of almost automorphic sequences, and the interplay between almost periodicity and almost automorphic has been exposed for the first time in light of operator theory, complex variable functions and harmonic analysis methods. As such, the time has come for a second edition to this work, which was one of the most cited books of the year 2001. This new edition clarifies and improves upon earlier materials, includes many relevant contributions and references in new and generalized concepts and methods, and answers the longtime open problem, "What is the number of almost automorphic functions that are not almost periodic in the sense of Bohr?" Open problems in non-locally convex valued almost periodic and almost automorphic functions are also indicated. As in the first edition, materials are presented in a simplified and rigorous way. Each chapter is concluded with bibliographical notes showing the original sources of the results and further reading.

Existence Theory For Nonlinear Ordinary Differential Equations

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Author : Donal O'Regan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Existence Theory For Nonlinear Ordinary Differential Equations written by Donal O'Regan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here.

Handbook Of Differential Equations Ordinary Differential Equations

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Author : A. Canada
language : en
Publisher: Elsevier
Release Date : 2006-08-21

Handbook Of Differential Equations Ordinary Differential Equations written by A. Canada and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-21 with Mathematics categories.

This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience. These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for reseach, learing and teaching. This volumes consists of seven chapters covering a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume. - Covers a variety of problems in ordinary differential equations - Pure mathematical and real world applications - Written for mathematicians and scientists of many related fields