Generalized Ordinary Differential Equations in Abstract Spaces and Applications - Hardcover

Hardcover

ISBN 10: 1119654939 ISBN 13: 9781119654933

Publisher: Wiley, 2021

Synopsis

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.

About this title

About the Author

Everaldo M. Bonotto, PhD, is Associate Professor in the Department of ­Applied Mathematics and Statistics, at ICMC-Universidade de São Paulo, São Carlos, SP, Brazil.

Márcia Federson, PhD, is Full Professor in the Department of Mathematics at ICMC-Universidade de São Paulo, São Carlos, SP, Brazil.

Jaqueline G. Mesquita, PhD, is Assistant Professor at Department of Mathematics at the University of Brasília, Brasília, DF, Brazil.

From the Back Cover

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.

From the Inside Flap

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.

Edition details

• Publisher: Wiley
• Publication date: 2021
• Language: English
• ISBN 10: 1119654939
• ISBN 13: 9781119654933
• Binding: Hardcover
• Edition number: 1
• Number of pages: 506
• Editor: Bonotto Everaldo M., Federson Marcia, Mesquita Jaqueline G.