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Mat. Sb., 1998, Volume 189, Number 6, Pages 3–32 (Mi msb320)  

This article is cited in 9 scientific papers (total in 9 papers)

Perturbation of a convex-valued operator by a set-valued map of Hammerstein type with non-convex values, and boundary-value problems for functional-differential inclusions

A. I. Bulgakov, L. I. Tkach

Tambov State University

Abstract: A functional inclusion in the space of continuous vector-valued functions on the interval $[a,b]$ is considered, the right-hand side of which is the sum of a convex-valued set-valued map and the product of a linear integral operator and a set-valued map with images convex with respect to switching. Estimates for the distance between a solution of this inclusion and a fixed continuous vector-valued function are obtained and the structure of the set of solutions of this inclusion is studied on the basis of these estimates. A result on the density of the solutions of this inclusion in the set of solutions of the 'convexized' inclusion is obtained and the 'bang-bang' principle for the original inclusion is established. This theory is applied to the study of the solution sets of boundary-value problems for functional-differential inclusions with non-convex right-hand sides.

DOI: https://doi.org/10.4213/sm320

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English version:
Sbornik: Mathematics, 1998, 189:6, 821–848

Bibliographic databases:

UDC: 517.9
MSC: Primary 34K99, 34A60; Secondary 47H04, 47H15
Received: 30.12.1996 and 12.02.1997

Citation: A. I. Bulgakov, L. I. Tkach, “Perturbation of a convex-valued operator by a set-valued map of Hammerstein type with non-convex values, and boundary-value problems for functional-differential inclusions”, Mat. Sb., 189:6 (1998), 3–32; Sb. Math., 189:6 (1998), 821–848

Citation in format AMSBIB
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\issue 6
\pages 3--32
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\pages 821--848
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Bulgakov, AI, “Ordinary differential inclusions with internal and external perturbations”, Differential Equations, 36:12 (2000), 1741  mathnet  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    2. A. I. Bulgakov, V. V. Skomorokhov, “Approximation of differential inclusions”, Sb. Math., 193:2 (2002), 187–203  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. 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
    4. Bulcakov, AI, “On approximation of the perturbed inclusion”, Georgian Mathematical Journal, 14:2 (2007), 253  mathscinet  isi
    5. Machina, A, “Generalized solutions of functional differential inclusions”, Abstract and Applied Analysis, 2008, 829701  mathscinet  zmath  isi
    6. Grigorenko A.A., Skomorokhov V.V., “Otsenka blizosti reshenii vozmuschennogo vklyucheniya k napered zadannym funktsiyam”, Vestnik tambovskogo universiteta. seriya: estestvennye i tekhnicheskie nauki, 16:1 (2011), 61–66  elib
    7. Tian Yu., Henderson J., “Three Anti-Periodic Solutions for Second-Order Impulsive Differential Inclusions via Nonsmooth Critical Point Theory”, Nonlinear Anal.-Theory Methods Appl., 75:18 (2012), 6496–6505  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    8. Nyamoradi N., Tian Yu., “Existence of Solutions For Second-Order Impulsive Differential Inclusions”, Math. Meth. Appl. Sci., 38:11 (2015), 2229–2242  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    9. Tian Yu., Graef J.R., Kong L., Wang M., “Three Solutions For Second-Order Impulsive Differential Inclusions With Sturm-Liouville Boundary Conditions Via Nonsmooth Critical Point Theory”, Topol. Methods Nonlinear Anal., 47:1 (2016), 1–17  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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