| Basic Topological Structures of Ordinary Differential Equations 1998 Edition Contributor(s): Filippov, V. V. (Author) |
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ISBN: 0792349512 ISBN-13: 9780792349518 Publisher: Springer OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: August 1998 Annotation: 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 consideration of 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. Audience: This volume will be of interest to graduate students and researchers whose work involves ordinary differential equations, functional analysis and general topology. |
| Additional Information |
| BISAC Categories: - Mathematics | Topology - General - Mathematics | Differential Equations - General |
| Dewey: 515.35 |
| LCCN: 97050330 |
| Series: Mathematics and Its Applications |
| Physical Information: 1.19" H x 6.14" W x 9.21" (2.04 lbs) 522 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: The aim of this book is a detailed study of topological effects related to continuity of the dependence of solutions on initial values and parameters. This allows us to develop cheaply a theory which deals easily with equations having singularities and with equations with multivalued right hand sides (differential inclusions). An explicit description of corresponding topological structures expands the theory in the case of equations with continuous right hand sides also. In reality, this is a new science where Ordinary Differential Equations, General Topology, Integration theory and Functional Analysis meet. In what concerns equations with discontinuities and differential inclu- sions, we do not restrict the consideration to the Cauchy problem, but we show how to develop an advanced theory whose volume is commensurable with the volume of the existing theory of Ordinary Differential Equations. The level of the account rises in the book step by step from second year student to working scientist. |