Solution Sets Of Differential Equations In Abstract Spaces
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| Author | : Robert Dragoni |
| Publisher | : CRC Press |
| Total Pages | : 42 |
| Release | : 1996-04-03 |
| Genre | : Mathematics |
| ISBN | : 9780582294509 |
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.
| Author | : Robert Dragoni |
| Publisher | : Chapman and Hall/CRC |
| Total Pages | : 120 |
| Release | : 1996-04-03 |
| Genre | : Mathematics |
| ISBN | : 9780582294509 |
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.
| Author | : Everaldo M. Bonotto |
| Publisher | : John Wiley & Sons |
| Total Pages | : 514 |
| Release | : 2021-09-15 |
| Genre | : Mathematics |
| ISBN | : 1119654939 |
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.
| Author | : V. Lakshmikantham |
| Publisher | : Pergamon |
| Total Pages | : 276 |
| Release | : 1981 |
| Genre | : Mathematics |
| ISBN | : |
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
| Author | : Yeol Je Cho |
| Publisher | : Nova Publishers |
| Total Pages | : 182 |
| Release | : 2007-07-02 |
| Genre | : Mathematics |
| ISBN | : 9781594548789 |
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.
| Author | : Lakshmikantham |
| Publisher | : Academic Press |
| Total Pages | : 231 |
| Release | : 1972-06-16 |
| Genre | : Computers |
| ISBN | : 0080955940 |
Differential Equations in Abstract Spaces
| Author | : V. Lakshmikantham |
| Publisher | : |
| Total Pages | : 224 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : |
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.
| Author | : Kai Liu |
| Publisher | : Cambridge University Press |
| Total Pages | : 277 |
| Release | : 2019-05-02 |
| Genre | : Mathematics |
| ISBN | : 1108705170 |
Presents a unified treatment of stochastic differential equations in abstract, mainly Hilbert, spaces.
| Author | : Robert W. Carroll |
| Publisher | : Courier Corporation |
| Total Pages | : 385 |
| Release | : 2013-05-27 |
| Genre | : Mathematics |
| ISBN | : 0486263282 |
Detailed, self-contained treatment examines modern abstract methods in partial differential equations, especially abstract evolution equations. Suitable for graduate students with some previous exposure to classical partial differential equations. 1969 edition.
| Author | : Ivan Gavrilyuk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 187 |
| Release | : 2011-07-17 |
| Genre | : Mathematics |
| ISBN | : 303480119X |
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.
