Solution Sets Of Differential Equations In Abstract Spaces

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Solution Sets of Differential Equations in Abstract Spaces

Robert Dragoni,Paolo Nistri,Pietro Zecca,Jack W Macki
Solution Sets of Differential Equations in Abstract Spaces Book PDF

Author : Robert Dragoni,Paolo Nistri,Pietro Zecca,Jack W Macki
Publisher : CRC Press
Page : 42 pages
File Size : 51,5 Mb
Release : 1996-04-03
Category : Mathematics
ISBN : 0582294509

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Solution Sets of Differential Equations in Abstract Spaces by Robert Dragoni,Paolo Nistri,Pietro Zecca,Jack W Macki Pdf

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

Robert Dragoni,Paolo Nistri,Pietro Zecca,Jack W Macki
Solution Sets of Differential Equations in Abstract Spaces Book PDF

Author : Robert Dragoni,Paolo Nistri,Pietro Zecca,Jack W Macki
Publisher : Chapman and Hall/CRC
Page : 120 pages
File Size : 51,5 Mb
Release : 1996-04-03
Category : Mathematics
ISBN : 0582294509

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Solution Sets of Differential Equations in Abstract Spaces by Robert Dragoni,Paolo Nistri,Pietro Zecca,Jack W Macki Pdf

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.

Generalized Ordinary Differential Equations in Abstract Spaces and Applications

Everaldo M. Bonotto,Márcia Federson,Jaqueline G. Mesquita
Generalized Ordinary Differential Equations in Abstract Spaces and Applications Book PDF

Author : Everaldo M. Bonotto,Márcia Federson,Jaqueline G. Mesquita
Publisher : John Wiley & Sons
Page : 512 pages
File Size : 49,7 Mb
Release : 2021-08-26
Category : Mathematics
ISBN : 9781119655008

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Generalized Ordinary Differential Equations in Abstract Spaces and Applications by Everaldo M. Bonotto,Márcia Federson,Jaqueline G. Mesquita Pdf

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.

Nonlinear Differential Equations in Abstract Spaces

V. Lakshmikantham,S. Leela
Nonlinear Differential Equations in Abstract Spaces Book PDF

Author : V. Lakshmikantham,S. Leela
Publisher : Pergamon
Page : 276 pages
File Size : 53,6 Mb
Release : 1981
Category : Mathematics
ISBN : UCAL:B4406400

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Nonlinear Differential Equations in Abstract Spaces by V. Lakshmikantham,S. Leela Pdf

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

Differential Equations and Applications

Yeol Je Cho
Differential Equations and Applications Book PDF

Author : Yeol Je Cho
Publisher : Nova Publishers
Page : 182 pages
File Size : 45,8 Mb
Release : 2007-07-02
Category : Mathematics
ISBN : 1594548781

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Differential Equations and Applications by Yeol Je Cho Pdf

Preface; Existence for set Differential Equations via Multivalued Operator Equations; Nonlocal Cauchy Problem for Abstract Functional Integrodifferential Equations; Existence Results for Discontinuous Functional Evolution Equations in Abstract Spaces; A Generalised Solution of the Black-Scholes Partial Differential Equation; Optimality and Duality for Multiobjective Fractional Programming with Generalised Invexity; Markovian Approach to the Backward Recurrence Time; A Multiplicity Result of Singular Boundary Value Problems for Second Order Impulsive Differential Equations; Extremal Solutions of Initial Value Problem for Non-linear Second Order Impulsive Integro-Differential Equations of Volterra Type in Banach Spaces; Construction of Upper and Lower Solutions for Singular p-Laplacian Equations with Sign Changing Nonlinearities; A Qualitative Hamiltonian Model for Human Motion; ; Newton's Method for Matrix Polynomials; Admissibility and Non-Uniform Dichotomy for Differential Systems; Boundary Value Problems of Fuzzy Differential Equations on an Infinite Interval; An Ultimate Boundedness Result for a Certain System of Fourth Order Non-linear Differential Equations; The Initial Value Problems for the First Order System of Non-linear Impulsive Integro-Differential Equations; Generic Well-Posedness of Nonconvex Optimal Control Problems; Index.

Theory of Set Differential Equations in Metric Spaces

V. Lakshmikantham,Tenali Gnana Bhaskar,J. Vasundhara Devi
Theory of Set Differential Equations in Metric Spaces Book PDF

Author : V. Lakshmikantham,Tenali Gnana Bhaskar,J. Vasundhara Devi
Publisher : Unknown
Page : 224 pages
File Size : 54,9 Mb
Release : 2006
Category : Mathematics
ISBN : STANFORD:36105126896096

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Theory of Set Differential Equations in Metric Spaces by V. Lakshmikantham,Tenali Gnana Bhaskar,J. Vasundhara Devi Pdf

The aim of this volume is to describe the theory of set differential equations (SDEs) as an independent discipline. It incorporates the recent general theory of set differential equations, discusses the interconnections between set differential equations and fuzzy differential equations and uses both smooth and nonsmooth analysis for investigation. The study of SDEs is a rapidly growing area of mathematics and this volume provides a timely introduction to a subject that follows the present trend of studying analysis and differential equations in metric spaces. It is a useful reference text for postgraduates and researchers/nonlinear analysts, engineering and computational scientists working in fuzzy systems.

Functional Analysis, Sobolev Spaces and Partial Differential Equations

Haim Brezis
Functional Analysis Sobolev Spaces and Partial Differential Equations Book PDF

Author : Haim Brezis
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 50,5 Mb
Release : 2010-11-02
Category : Mathematics
ISBN : 9780387709147

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Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis Pdf

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.

Almost Periodic Solutions of Differential Equations in Banach Spaces

Yoshiyuki Hino,Toshiki Naito,Nguyen VanMinh,Jong Son Shin
Almost Periodic Solutions of Differential Equations in Banach Spaces Book PDF

Author : Yoshiyuki Hino,Toshiki Naito,Nguyen VanMinh,Jong Son Shin
Publisher : CRC Press
Page : 276 pages
File Size : 47,6 Mb
Release : 2001-10-25
Category : Mathematics
ISBN : 0415272661

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Almost Periodic Solutions of Differential Equations in Banach Spaces by Yoshiyuki Hino,Toshiki Naito,Nguyen VanMinh,Jong Son Shin Pdf

This monograph presents recent developments in spectral conditions for the existence of periodic and almost periodic solutions of inhomogenous equations in Banach Spaces. Many of the results represent significant advances in this area. In particular, the authors systematically present a new approach based on the so-called evolution semigroups with an original decomposition technique. The book also extends classical techniques, such as fixed points and stability methods, to abstract functional differential equations with applications to partial functional differential equations. Almost Periodic Solutions of Differential Equations in Banach Spaces will appeal to anyone working in mathematical analysis.

Solution Sets for Differential Equations and Inclusions

Smaïl Djebali,Lech Górniewicz,Abdelghani Ouahab
Solution Sets for Differential Equations and Inclusions Book PDF

Author : Smaïl Djebali,Lech Górniewicz,Abdelghani Ouahab
Publisher : ISSN
Page : 0 pages
File Size : 53,7 Mb
Release : 2013
Category : Boundary value problems
ISBN : 3110293447

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

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-Chief Jürgen Appell, Würzburg, Germany Honorary and Advisory Editors Catherine Bandle, Basel, Switzerland Jiguang Bao, Beijing, China Avner Friedman, Columbus, Ohio, USA Manuel del Pino, Bath, UK, and Santiago, Chile Mikio Kato, Nagano, Japan Guozhen Lu, Storrs, CT, USA Wojciech Kryszewski, Toruń, Poland Vicenţiu D. Rădulescu, Kraków, Poland Simeon Reich, Haifa, Israel Please submit book proposals to Jürgen Appell. Titles in planning include Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy-Leray Potential (2020) Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020) Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)

Topics on Stability and Periodicity in Abstract Differential Equations

Gaston M. N'Guerekata
Topics on Stability and Periodicity in Abstract Differential Equations Book PDF

Author : Gaston M. N'Guerekata
Publisher : World Scientific
Page : 219 pages
File Size : 50,8 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812818249

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Topics on Stability and Periodicity in Abstract Differential Equations by Gaston M. N'Guerekata Pdf

This book presents recent methods of study on the asymptotic behavior of solutions of abstract differential equations such as stability, exponential dichotomy, periodicity, almost periodicity, and almost automorphy of solutions. The chosen methods are described in a way that is suitable to those who have some experience with ordinary differential equations. The book is intended for graduate students and researchers in the related areas.

Exponentially Convergent Algorithms for Abstract Differential Equations

Ivan Gavrilyuk,Volodymyr Makarov,Vitalii Vasylyk
Exponentially Convergent Algorithms for Abstract Differential Equations Book PDF

Author : Ivan Gavrilyuk,Volodymyr Makarov,Vitalii Vasylyk
Publisher : Springer Science & Business Media
Page : 187 pages
File Size : 49,6 Mb
Release : 2011-07-17
Category : Mathematics
ISBN : 9783034801195

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Exponentially Convergent Algorithms for Abstract Differential Equations by Ivan Gavrilyuk,Volodymyr Makarov,Vitalii Vasylyk Pdf

This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as of partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which then can be applied to mathematical models of the real world. The problem class includes initial value problems (IVP) for first order differential equations with constant and variable unbounded operator coefficients in a Banach space (the heat equation is a simple example), boundary value problems for the second order elliptic differential equation with an operator coefficient (e.g. the Laplace equation), IVPs for the second order strongly damped differential equation as well as exponentially convergent methods to IVPs for the first order nonlinear differential equation with unbounded operator coefficients. For researchers and students of numerical functional analysis, engineering and other sciences this book provides highly efficient algorithms for the numerical solution of differential equations and applied problems.

Polynomial Operator Equations in Abstract Spaces and Applications

Ioannis K. Argyros
Polynomial Operator Equations in Abstract Spaces and Applications Book PDF

Author : Ioannis K. Argyros
Publisher : CRC Press
Page : 598 pages
File Size : 41,9 Mb
Release : 2020-10-07
Category : Mathematics
ISBN : 9781000142457

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Polynomial Operator Equations in Abstract Spaces and Applications by Ioannis K. Argyros Pdf

Polynomial operators are a natural generalization of linear operators. Equations in such operators are the linear space analog of ordinary polynomials in one or several variables over the fields of real or complex numbers. Such equations encompass a broad spectrum of applied problems including all linear equations. Often the polynomial nature of many nonlinear problems goes unrecognized by researchers. This is more likely due to the fact that polynomial operators - unlike polynomials in a single variable - have received little attention. Consequently, this comprehensive presentation is needed, benefiting those working in the field as well as those seeking information about specific results or techniques. Polynomial Operator Equations in Abstract Spaces and Applications - an outgrowth of fifteen years of the author's research work - presents new and traditional results about polynomial equations as well as analyzes current iterative methods for their numerical solution in various general space settings. Topics include: Special cases of nonlinear operator equations Solution of polynomial operator equations of positive integer degree n Results on global existence theorems not related with contractions Galois theory Polynomial integral and polynomial differential equations appearing in radiative transfer, heat transfer, neutron transport, electromechanical networks, elasticity, and other areas Results on the various Chandrasekhar equations Weierstrass theorem Matrix representations Lagrange and Hermite interpolation Bounds of polynomial equations in Banach space, Banach algebra, and Hilbert space The materials discussed can be used for the following studies Advanced numerical analysis Numerical functional analysis Functional analysis Approximation theory Integral and differential equation

Stochastic Stability of Differential Equations in Abstract Spaces

Kai Liu
Stochastic Stability of Differential Equations in Abstract Spaces Book PDF

Author : Kai Liu
Publisher : Cambridge University Press
Page : 277 pages
File Size : 55,6 Mb
Release : 2019-05-02
Category : Mathematics
ISBN : 9781108705172

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Stochastic Stability of Differential Equations in Abstract Spaces by Kai Liu Pdf

Presents a unified treatment of stochastic differential equations in abstract, mainly Hilbert, spaces.

Theory of Integro-Differential Equations

V. Lakshmikantham
Theory of Integro Differential Equations Book PDF

Author : V. Lakshmikantham
Publisher : CRC Press
Page : 376 pages
File Size : 40,6 Mb
Release : 1995-03-15
Category : Mathematics
ISBN : 2884490000

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Theory of Integro-Differential Equations by V. Lakshmikantham Pdf

This unique monograph investigates the theory and applications of Volterra integro-differential equations. Whilst covering the basic theory behind these equations it also studies their qualitative properties and discusses a large number of applications. This comprehensive work presents a unified framework to investigate the fundamental existence of theory, treats stability theory in terms of Lyapunov functions and functionals, develops the theory of integro-differential equations with impulse effects, and deals with linear evolution equations in abstract spaces. Various applications of integro-differential equations, such as population dynamics, nuclear reactors, viscoelasticity, wave propagation and engineering systems, are discussed, making this book indispensable for mathematicians and engineers alike.

Topics in Abstract Differential Equations II

S D Zaidman
Topics in Abstract Differential Equations II Book PDF

Author : S D Zaidman
Publisher : CRC Press
Page : 184 pages
File Size : 41,6 Mb
Release : 1995-03-20
Category : Mathematics
ISBN : 0582253403

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Topics in Abstract Differential Equations II by S D Zaidman Pdf

This looks at a new branch of operator theory and partial differential equations, which in recent years, has become a rapidly growing field of mathematics. Well-posed problems are studied in the context of the theory of operator groups and semigroups as well as the framework of time dependent evolution equations. Non well-posed problems are also considered.