Basic Topological Structures of Ordinary Differential Equations

By: V.V. Filippov

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Hardcover | 31 August 1998

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540 Pages

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24.77 x 17.15 x 3.81

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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.

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Preface
Topological and Metric Spaces	p. 1
Some Properties of Topological, Metric and Euclidean Spaces	p. 37
Spaces of Mappings and Spaces of Compact Subsets	p. 71
Derivation and Integration	p. 95
Weak Topology on the Space L[subscript 1] and Derivation of Convergent Sequences	p. 163
Basic Properties of Solution Spaces	p. 191
Convergent Sequences of Solution Spaces	p. 209
Peano, Caratheodory and Davy Conditions	p. 247
Comparison Theorem	p. 277
Changes of Variables, Morphisms and Maximal Extensions	p. 291
Some Methods of Investigation of Equations	p. 327
Equations and Inclusions with Complicated Discontinuities in the Space Variables	p. 357
Equations and Inclusions of Second Order. Cauchy Problem Theory	p. 389
Equations and Inclusions of Second Order. Periodic Solutions, Dirichlet Problem	p. 409
Behavior of Solutions	p. 441
Two-Dimensional Systems	p. 469
References	p. 507
Index	p. 510
Notation	p. 515
Table of Contents provided by Blackwell. All Rights Reserved.

Basic Topological Structures of Ordinary Differential Equations

At a Glance

Hardcover

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Paperback

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