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Basic Topological Structures of Ordinary Differential Equations

  • V. V. Filippov

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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. V. V. Filippov
    Pages 1-36
  3. V. V. Filippov
    Pages 95-162
  4. V. V. Filippov
    Pages 191-208
  5. V. V. Filippov
    Pages 209-246
  6. V. V. Filippov
    Pages 247-276
  7. V. V. Filippov
    Pages 277-290
  8. V. V. Filippov
    Pages 327-356
  9. V. V. Filippov
    Pages 441-468
  10. V. V. Filippov
    Pages 469-506
  11. Back Matter
    Pages 507-522

About this book

Introduction

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.

Keywords

Cauchy problem differential equation differential inclusions functional analysis integration ordinary differential equation topology

Authors and affiliations

  • V. V. Filippov
    • 1
  1. 1.Department of MathematicsMoscow State UniversityMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-0841-8
  • Copyright Information Springer Science+Business Media B.V. 1998
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4995-7
  • Online ISBN 978-94-017-0841-8
  • Buy this book on publisher's site
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