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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."
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."
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