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Mat. Sb., 1992, Volume 183, Number 10, Pages 63–86 (Mi msb1080)  

This article is cited in 12 scientific papers (total in 12 papers)

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

A. I. Bulgakov

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.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1994, 77:1, 193–212

Bibliographic databases:

UDC: 517.9
MSC: Primary 34A60, 54C60; Secondary 49J30, 45D05, 45P05, 49K24, 54C65
Received: 19.08.1991

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
\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
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 77
\issue 1
\pages 193--212

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    This publication is cited in the following articles:
    1. 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”, Sb. Math., 189:6 (1998), 821–848  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. I. Bulgakov, L. I. Tkach, “Perturbation of a single-valued operator by a multi-valued mapping of Hammerstein type with nonconvex images”, Russian Math. (Iz. VUZ), 43:3 (1999), 1–13  mathnet  mathscinet  zmath  elib
    3. Bulgakov, AI, “Ordinary differential inclusions with internal and external perturbations”, Differential Equations, 36:12 (2000), 1741  mathnet  crossref  mathscinet  zmath  isi
    4. C Corduneanu, “Abstract Volterra Equations: A Survey”, Mathematical and Computer Modelling, 32:11-13 (2000), 1503  crossref  mathscinet  zmath
    5. A. I. Bulgakov, V. V. Skomorokhov, “Approximation of differential inclusions”, Sb. Math., 193:2 (2002), 187–203  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. Nguyen H., “Semicontinuity and Continuous Selections for the Multivalued Superposition Operator Without Assuming Growth-Type Conditions”, Studia Math., 163:1 (2004), 1–19  crossref  mathscinet  zmath  isi
    7. 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
    8. Machina, A, “Generalized solutions of functional differential inclusions”, Abstract and Applied Analysis, 2008, 829701  mathscinet  zmath  isi
    9. 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  elib
    10. 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
    11. 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
    12. G. E. Abduragimov, P. E. Abduragimova, M. M. Kuramagomedova, “O suschestvovanii i edinstvennosti polozhitelnogo resheniya kraevoi zadachi dlya nelineinogo obyknovennogo differentsialnogo uravneniya chetnogo poryadka”, Vestnik rossiiskikh universitetov. Matematika, 26:136 (2021), 341–347  mathnet  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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