Generalized Ordinary Differential Equations in Abstract Spaces and Applications

Everaldo M. Bonotto, Márcia Federson, Jaqueline G. Mesquita, Everaldo M. Bonotto, Márcia Federson, Jaqueline G. Mesquita

• Publisher: Wiley
• Year: 2021
• ISBN:
  9781119654940
• Edition: 1
• Topic: Mathematik
• Subtopic: Abstrakte Algebra

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 compactsets
• 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.

Table of contents

• Cover
• Title Page
• Copyright
• Contents
• List of Contributors
• Foreword
• Preface
• Chapter 1 Preliminaries
• Chapter 2 The Kurzweil Integral
• Chapter 3 Measure Functional Differential Equations
• Chapter 4 Generalized Ordinary Differential Equations
• Chapter 5 Basic Properties of Solutions
• Chapter 6 Linear Generalized Ordinary Differential Equations
• Chapter 7 Continuous Dependence on Parameters
• Chapter 8 Stability Theory
• Chapter 9 Periodicity
• Chapter 10 Averaging Principles
• Chapter 11 Boundedness of Solutions
• Chapter 12 Control Theory
• Chapter 13 Dichotomies
• Chapter 14 Topological Dynamics
• Chapter 15 Applications to Functional Differential Equations of Neutral Type
• References
• List of Symbols
• Index
• EULA