Basic Topological Structures Of Ordinary Differential Equations; Author: Filippov, V. V.; Hardback; Book

Author: Filippov, V. V.
Series#:432; Mathematics & Its Applications (Numbered Hardcover); Hardback; Book; References, Index
532 pages
Published: January 1998
Kluwer Academic Publishers Group
ISBN: 0792349512
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Traditionally, equations with discontinuities in space variables follow the ideology of the 'sliding mode'. This book contains the first account of the theory which allows the considerationof exact solutions for such equations. The difference between the two approaches is illustrated by scalar equations of the type y=f(y) and by equations arising under the synthesis of optimal control.A detailed study of topological effects related to limit passages in ordinary differential equations widens the theory for the case of equations with continuous right-hand sides, and makes it possible to work easily with equations with complicated discontinuities in their right-hand sides and with differential inclusions.This volume will be of interest to graduate students and researchers whoseTraditionally, equations with discontinuities in space variables follow the ideology of the sliding mode. This book contains the first account of the theory which allows the consideration of exact solutions for such equations.