RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb., 2005, Volume 196, Number 2, Pages 117–138 (Mi msb1269)  

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

Bogolyubov's theorem under constraints generated by a lower semicontinuous differential inclusion

A. A. Tolstonogov

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences

Abstract: An analogue of the classical theorem of Bogolyubov with non-convex constraint is proved. The constraint is the solution set of a differential inclusion with non-convex lower semicontinuous right-hand side. As an application we study the interrelation between the solutions of the problem of minimizing an integral functional with non-convex integrand on the solutions of the original inclusion and the solutions of the relaxation problem.

DOI: https://doi.org/10.4213/sm1269

Full text: PDF file (370 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2005, 196:2, 263–285

Bibliographic databases:

UDC: 517.972
MSC: Primary 49J45; Secondary 34A60, 49J24
Received: 16.02.2004

Citation: A. A. Tolstonogov, “Bogolyubov's theorem under constraints generated by a lower semicontinuous differential inclusion”, Mat. Sb., 196:2 (2005), 117–138; Sb. Math., 196:2 (2005), 263–285

Citation in format AMSBIB
\Bibitem{Tol05}
\by A.~A.~Tolstonogov
\paper Bogolyubov's theorem under constraints generated by a~lower semicontinuous differential inclusion
\jour Mat. Sb.
\yr 2005
\vol 196
\issue 2
\pages 117--138
\mathnet{http://mi.mathnet.ru/msb1269}
\crossref{https://doi.org/10.4213/sm1269}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2142492}
\zmath{https://zbmath.org/?q=an:1089.34013}
\elib{https://elibrary.ru/item.asp?id=9135675}
\transl
\jour Sb. Math.
\yr 2005
\vol 196
\issue 2
\pages 263--285
\crossref{https://doi.org/10.1070/SM2005v196n02ABEH000880}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000229078800011}
\elib{https://elibrary.ru/item.asp?id=13473782}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-18944361873}


Linking options:
  • http://mi.mathnet.ru/eng/msb1269
  • https://doi.org/10.4213/sm1269
  • http://mi.mathnet.ru/eng/msb/v196/i2/p117

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. Jiang Y.-r., Huang N.-j., Zhang Q.-f., Shang Ch.-ch., “Relaxation in Nonconvex Optimal Control Problems Governed By Evolution Inclusions With the Difference of Two Clarke'S Subdifferentials”, Int. J. Control  crossref  isi  scopus
    2. D. V. Khlopin, “Euler's broken lines in systems with Carathéodory conditions”, Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S141–S158  mathnet  crossref  elib
    3. D. V. Khlopin, “Euler polygons in systems with time-measurable right-hand side”, Differ. Equ., 44:12 (2008), 1711–1720  crossref  mathscinet  mathscinet  zmath  isi  elib  elib
    4. Tolstonogov A.A., “Existence and relaxation theorems for extreme continuous selectors of multifunctions with decomposable values”, Topology Appl., 155:8 (2008), 898–905  crossref  mathscinet  zmath  isi  elib
    5. S. A. Timoshin, A. A. Tolstonogov, “Bogolyubov-type theorem with constraints induced by a control system with hysteresis effect”, Nonlinear Anal., 75:15 (2012), 5884  crossref  mathscinet  zmath  isi  elib
    6. Xiaoyou Liu, Zhenhai Liu, “Relaxation control for a class of evolution hemivariational inequalities”, Isr. J. Math., 202:1 (2014), 35–58  crossref  mathscinet  zmath  isi
    7. Liu X. Xu Y., “Bogolyubov-Type Theorem with Constraints Generated by a Fractional Control System”, Fract. Calc. Appl. Anal., 19:1 (2016), 94–115  crossref  mathscinet  zmath  isi  scopus
    8. Tolstonogov A.A., “Relaxation in Nonconvex Optimal Control Problems Containing the Difference of Two Subdifferentials”, SIAM J. Control Optim., 54:1 (2016), 175–197  crossref  mathscinet  zmath  isi  scopus
    9. Li X., Liu Zh., “Relaxation in Nonconvex Optimal Control Problems For Nonautonomous Fractional Evolution Equations”, Pac. J. Optim., 13:3 (2017), 443–462  mathscinet  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:295
    Full text:126
    References:59
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020