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Basic Topological Structures of Ordinary Differential Equations

  • Book
  • © 1998

Overview

Authors:
  1. V. V. Filippov

    1. Department of Mathematics, Moscow State University, Moscow, Russia

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Part of the book series: Mathematics and Its Applications (MAIA, volume 432)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Topological and Metric Spaces

    • V. V. Filippov
    Pages 1-36

  3. Some Properties of Topological, Metric and Euclidean Spaces

    • V. V. Filippov
    Pages 37-70

  4. Spaces of Mappings and Spaces of Compact Subsets

    • V. V. Filippov
    Pages 71-94

  5. Derivation and Integration

    • V. V. Filippov
    Pages 95-162

  6. Weak Topology on the Space L 1 and Derivation of Convergent Sequences

    • V. V. Filippov
    Pages 163-190

  7. Basic Properties of Solution Spaces

    • V. V. Filippov
    Pages 191-208

  8. Convergent Sequences of Solution Spaces

    • V. V. Filippov
    Pages 209-246

  9. Peano, Caratheodory and Davy Conditions

    • V. V. Filippov
    Pages 247-276

  10. Comparison Theorem

    • V. V. Filippov
    Pages 277-290

  11. Changes of Variables, Morphisms and Maximal Extensions

    • V. V. Filippov
    Pages 291-326

  12. Some Methods of Investigation of Equations

    • V. V. Filippov
    Pages 327-356

  13. Equations and Inclusions with Complicated Discontinuities in the Space Variables

    • V. V. Filippov
    Pages 357-388

  14. Equations and Inclusions of Second Order. Cauchy Problem Theory

    • V. V. Filippov
    Pages 389-408

  15. Equations and Inclusions of Second Order. Periodic Solutions, Dirichlet Problem

    • V. V. Filippov
    Pages 409-440

  16. Behavior of Solutions

    • V. V. Filippov
    Pages 441-468

  17. Two-Dimensional Systems

    • V. V. Filippov
    Pages 469-506

  18. Back Matter

    Pages 507-522
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, Moscow State University, Moscow, Russia

    V. V. Filippov

Bibliographic Information

  • Book Title: Basic Topological Structures of Ordinary Differential Equations

  • Authors: V. V. Filippov

  • Series Title: Mathematics and Its Applications

  • DOI: https://doi.org/10.1007/978-94-017-0841-8

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1998

  • Hardcover ISBN: 978-0-7923-4951-8Published: 31 August 1998

  • Softcover ISBN: 978-90-481-4995-7Published: 08 December 2010

  • eBook ISBN: 978-94-017-0841-8Published: 09 March 2013

  • Edition Number: 1

  • Number of Pages: XIV, 522

  • Number of Illustrations: 9 b/w illustrations

  • Topics: Ordinary Differential Equations, Functional Analysis, Topology

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