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Mat. Sb., 2005, Volume 196, Number 10, Pages 21–78 (Mi msb1425)  

This article is cited in 5 scientific papers (total in 5 papers)

On the theory of perturbed inclusions and its applications

A. I. Bulgakov, O. P. Belyaeva, A. A. Grigorenko

Tambov State University

Abstract: Inclusions with right-hand side that is the algebraic sum of the values of a compact-valued operator and a map equal to the product of a linear integral operator and a set-valued operator with values convex with respect to switching are considered. Existence questions for solutions of such inclusions are discussed, and the density principle and the ‘bang-bang’ principle are established. Properties of the solution sets of inclusions with internal and external perturbations are studied. A necessary and sufficient condition ensuring that the intersection of the closures of the sets of approximate solutions coincides with the closure of the set of the original inclusion is obtained. The results are applied to the analysis of boundary-value problems for functional-differential inclusions.

DOI: https://doi.org/10.4213/sm1425

Full text: PDF file (609 kB)
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English version:
Sbornik: Mathematics, 2005, 196:10, 1421–1472

Bibliographic databases:

UDC: 517.9
MSC: Primary 47H04; Secondary 28B20, 34A60
Received: 20.04.2004 and 22.11.2004

Citation: A. I. Bulgakov, O. P. Belyaeva, A. A. Grigorenko, “On the theory of perturbed inclusions and its applications”, Mat. Sb., 196:10 (2005), 21–78; Sb. Math., 196:10 (2005), 1421–1472

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm1425
  • http://mi.mathnet.ru/eng/msb/v196/i10/p21

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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, A. I. Polyanskii, “Nekotorye svoistva reshenii obobschenno ovypuklennogo vozmuschennogo vklyucheniya”, Izv. IMI UdGU, 2006, no. 2(36), 17–20  mathnet
    2. A. I. Korobko, “Printsip plotnosti i approksimatsiya vozmuschennogo vklyucheniya”, Izv. IMI UdGU, 2006, no. 3(37), 69–70  mathnet
    3. A. I. Polyanskii, “Obobschenno ekstremalnye kvaziresheniya vozmuschennykh vklyuchenii”, Izv. IMI UdGU, 2006, no. 3(37), 127–128  mathnet
    4. 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
    5. Machina A., Bulgakov A., Grigorenko A., “Generalized solutions of functional differential inclusions”, Abstr. Appl. Anal., 2008, 829701, 35 pp.  mathscinet  zmath  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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