Differential Inclusions in a Banach Space

  • Alexander Tolstonogov

Part of the Mathematics and Its Applications book series (MAIA, volume 524)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Alexander Tolstonogov
    Pages 63-129
  3. Alexander Tolstonogov
    Pages 131-184
  4. Alexander Tolstonogov
    Pages 185-234
  5. Alexander Tolstonogov
    Pages 235-254
  6. Back Matter
    Pages 255-302

About this book


Preface to the English Edition The present monograph is a revised and enlarged alternative of the author's monograph [19] which was devoted to the development of a unified approach to studying differential inclusions, whose values of the right hand sides are compact, not necessarily convex subsets of a Banach space. This approach relies on ideas and methods of modem functional analysis, general topology, the theory of multi-valued mappings and continuous selectors. Although the basic content of the previous monograph has been remained the same this monograph has been partly re-organized and the author's recent results have been added. The contents of the present book are divided into five Chapters and an Appendix. The first Chapter of the J>ook has been left without changes and deals with multi-valued differential equations generated by a differential inclusion. The second Chapter has been significantly revised and extended. Here the au­ thor's recent results concerning extreme continuous selectors of multi-functions with decomposable values, multi-valued selectors ofmulti-functions generated by a differential inclusion, the existence of solutions of a differential inclusion, whose right hand side has different properties of semicontinuity at different points, have been included. Some of these results made it possible to simplify schemes for proofs concerning the existence of solutions of differential inclu­ sions with semicontinuous right hand side a.nd to obtain new results. In this Chapter the existence of solutions of different types are considered.


Banach space Mathematica differential equation differential inclusions functional analysis ordinary differential equation topology

Authors and affiliations

  • Alexander Tolstonogov
    • 1
  1. 1.Institute of System Dynamics and Control TheorySiberian Branch of the Russian Academy of SciencesIrkutskRussia

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media B.V. 2000
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5580-4
  • Online ISBN 978-94-015-9490-5
  • Buy this book on publisher's site
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