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Mat. Sb., 2002, Volume 193, Number 2, Pages 35–52 (Mi msb626)  

This article is cited in 7 scientific papers (total in 7 papers)

Approximation of differential inclusions

A. I. Bulgakova, V. V. Skomorokhovb

a Tambov State University
b Tambov State Technical University

Abstract: Methods for the approximation of a differential inclusion with right-hand side satisfying the Carathéodory conditions are considered. Necessary and sufficient conditions are obtained for the stability of the approximation of a differential inclusion under internal and external perturbations, which means that “small” changes (in the sense of the Hausdorff distance) of the right-hand side of the inclusion result in a “small” change of the solution set.

DOI: https://doi.org/10.4213/sm626

Full text: PDF file (336 kB)
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English version:
Sbornik: Mathematics, 2002, 193:2, 187–203

Bibliographic databases:

UDC: 517.911
MSC: 34A60, 34D09
Received: 31.01.2001

Citation: A. I. Bulgakov, V. V. Skomorokhov, “Approximation of differential inclusions”, Mat. Sb., 193:2 (2002), 35–52; Sb. Math., 193:2 (2002), 187–203

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. I. Bulgakov, O. P. Belyaeva, A. A. Grigorenko, “On the theory of perturbed inclusions and its applications”, Sb. Math., 196:10 (2005), 1421–1472  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. I. Korobko, “Printsip plotnosti i approksimatsiya vozmuschennogo vklyucheniya”, Izv. IMI UdGU, 2006, no. 3(37), 69–70  mathnet
    3. Bulcakov A.I., Grigorenko A.A., Korobko A.I., “On approximation of the perturbed inclusion”, Georgian Math. J., 14:2 (2007), 253–267  mathscinet  isi
    4. Donchev T., Farkhi E., Reich S., “Discrete approximations and fixed set iterations in Banach spaces”, SIAM J. Optim., 18:3 (2007), 895–906  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Machina A., Bulgakov A., Grigorenko A., “Generalized solutions of functional differential inclusions”, Abstr. Appl. Anal., 2008, 829701, 35 pp.  mathscinet  zmath  isi  elib
    6. Bulgakov A.I., Skomorokhov V.V., Filippova O.V., “Asimptoticheskie svoistva mnozhestva -reshenii differentsialnogo vklyucheniya s impulsnymi vozdeistviyami”, Vestnik tambovskogo universiteta. seriya: estestvennye i tekhnicheskie nauki, 16:4 (2011), 1039–1043  mathscinet  elib
    7. Bulgakov A.I., Skomorokhov V.V., Filippova O.V., “Approksimatsiya funktsionalno-differentsialnogo vklyucheniya s impulsnymi vozdeistviyami i vnutrennimi i vneshnimi vozmuscheniyami”, Vestnik tambovskogo universiteta. seriya: estestvennye i tekhnicheskie nauki, 17:1 (2012), 32–37  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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