Basic Topological Structures of Ordinary Differential Equations: 432 (Mathematics and Its Applications, 432) - Hardcover

Filippov, V.V.

Hardcover

ISBN 10: 0792349512 ISBN 13: 9780792349518

Publisher: Springer, 1998

Synopsis

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.

About this title

Synopsis

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. This volume should be of interest to graduate students and researchers whose work involves ordinary differential equations, functional analysis and general topology.

Edition details

• Publisher: Springer
• Publication date: 1998
• Language: English
• ISBN 10: 0792349512
• ISBN 13: 9780792349518
• Binding: Hardcover
• Number of pages: 536