Theory Of Abstract Spaces
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Nonlinear Equations in Abstract Spaces
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.
Analysis at Urbana: Volume 2, Analysis in Abstract Spaces
Author: Earl R. Berkson
language: en
Publisher: Cambridge University Press
Release Date: 1989-03-30
Throughout the acedemic year 1986-7, the University of Illinois hosted a symposium on mathematical analysis attended by some of the leading figures in the field. This resulting book lays emphasis on the synthesis of modern and classical analysis. The contributed articles cover the mainstream topics and will be essential to researchers in mathematical analysis.
Generalized Ordinary Differential Equations in Abstract Spaces and Applications
Author: Everaldo M. Bonotto
language: en
Publisher: John Wiley & Sons
Release Date: 2021-08-26
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.