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Russian Academy of Sciences. Sbornik. Mathematics, 1994, Volume 77, Issue 1, Pages 193–212
DOI: https://doi.org/10.1070/SM1994v077n01ABEH003436
(Mi sm1080)
 

This article is cited in 13 scientific papers (total in 13 papers)

Integral inclusions with nonconvex images, and their applications to boundary value problems for differential inclusions

A. I. Bulgakov
References:
Abstract: This paper contains a treatment of an integral inclusion of Hammerstein type generated by the product of a linear integral operator and a multivalued mapping with images convex with respect to switching. This product is not a Volterra operator in general. Estimates of the closeness of a solution of the inclusion to a given function are proved on the basis of the theory of existence of continuous branches of multivalued mappings with images convex with respect to switching. By using these estimates it is proved that the solution set of the original inclusion is dense in the solution set of the convexified inclusion in the space of continuous functions. In the case when the kernel of the linear operator consists solely of the zero element the 'bang-bang' principle is proved for the Hammerstein inclusion. In the second part of the paper the theory is used for investigating boundary value problems for differential inclusions with nonconvex right-hand side.
Received: 19.08.1991
Russian version:
Matematicheskii Sbornik, 1992, Volume 183, Number 10, Pages 63–86
Bibliographic databases:
UDC: 517.9
MSC: Primary 34A60, 54C60; Secondary 49J30, 45D05, 45P05, 49K24, 54C65
Language: English
Original paper language: Russian
Citation: A. I. Bulgakov, “Integral inclusions with nonconvex images, and their applications to boundary value problems for differential inclusions”, Mat. Sb., 183:10 (1992), 63–86; Russian Acad. Sci. Sb. Math., 77:1 (1994), 193–212
Citation in format AMSBIB
\Bibitem{Bul92}
\by A.~I.~Bulgakov
\paper Integral inclusions with nonconvex images, and their applications to boundary value problems for differential inclusions
\jour Mat. Sb.
\yr 1992
\vol 183
\issue 10
\pages 63--86
\mathnet{http://mi.mathnet.ru/sm1080}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1202792}
\zmath{https://zbmath.org/?q=an:0789.34020|0772.34017}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1994SbMat..77..193B}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 77
\issue 1
\pages 193--212
\crossref{https://doi.org/10.1070/SM1994v077n01ABEH003436}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1994MZ10900012}
Linking options:
  • https://www.mathnet.ru/eng/sm1080
  • https://doi.org/10.1070/SM1994v077n01ABEH003436
  • https://www.mathnet.ru/eng/sm/v183/i10/p63
  • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:450
    Russian version PDF:141
    English version PDF:24
    References:67
    First page:1
     
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