Overview

The contemporary approach of J Kurzweil and R Henstock to the Perron integral is applied to the theory of ordinary differential equations in this book. It focuses mainly on the problems of continuous dependence on parameters for ordinary differential equations. For this purpose, a generalized form of the integral based on integral sums is defined. The theory of generalized differential equations based on this integral is then used, for example, to cover differential equations with impulses or measure differential equations. Solutions of generalized differential equations are found to be functions of bounded variations.The book may be used for a special undergraduate course in mathematics or as a postgraduate text. As there are currently no other special research monographs or textbooks on this topic in English, this book is an invaluable reference text for those interested in this field.Request Inspection CopyContents: The Generalized Perron IntegralOrdinary Differential Equations and the Perron IntegralGeneralized Ordinary Differential EquationsExistence and Uniqueness of Solutions of Generalized Differential EquationsGeneralized Differential Equations and Other Concepts of Differential SystemsGeneralized Linear Differential EquationsProduct Integration and Generalized Linear Differential EquationsContinuous Dependence on Parameters for Generalized Ordinary Differential EquationsEmphatic Convergence for Generalized Ordinary Differential EquationsVariational Stability for Generalized Ordinary Differential EquationsReadership: Mathematicians, undergraduate and postgraduate students.

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