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.
