Generalized Ordinary Differential Equations (Series in Real Analysis)

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.

"... the book is highly recommended to researchers ... and to readers who wish to learn an important chapter in the philosophy and thinking of differential equations." Zvi Artstein Mathematical Reviews "... the book is well-written and organized ... warmly recommended to specialists working in differential equations ... every reader may find the book helpful as an introduction to the theory of generalized integrals and as a guide to the literature for futher details." J Bana Mathematics Abstracts