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Mat. Zametki, 2006, Volume 79, Issue 4, Pages 483–487 (Mi mz2719)  

This article is cited in 17 scientific papers (total in 17 papers)

On a weakened Cauchy problem for a linear differential inclusion

M. S. Bichegkuev

North-Ossetia State University

Abstract: For a differential inclusion $\dot x(t)\in\mathscr A x(t)$ with linear relation $\mathscr A$, we establish the connection between a weakened and the ordinary Cauchy problem. We prove the uniqueness of and the representation for the weakened solution.

DOI: https://doi.org/10.4213/mzm2719

Full text: PDF file (171 kB)
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English version:
Mathematical Notes, 2006, 79:4, 449–453

Bibliographic databases:

UDC: 517.98
Received: 21.12.2004

Citation: M. S. Bichegkuev, “On a weakened Cauchy problem for a linear differential inclusion”, Mat. Zametki, 79:4 (2006), 483–487; Math. Notes, 79:4 (2006), 449–453

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. M. S. Bichegkuev, “Conditions for solubility of difference inclusions”, Izv. Math., 72:4 (2008), 647–658  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. M. S. Bichegkuev, “On bounded solutions of difference inclusions”, Russian Math. (Iz. VUZ), 52:8 (2008), 12–19  mathnet  crossref  mathscinet  zmath  elib
    3. M. S. Bichegkuev, “O spektre raznostnykh i differentsialnykh operatorov v vesovykh prostranstvakh”, Funkts. analiz i ego pril., 44:1 (2010), 80–83  mathnet  crossref  mathscinet  zmath
    4. M. S. Bichegkuev, “To the theory of infinitely differentiable semigroups of operators”, St. Petersburg Math. J., 22:2 (2011), 175–182  mathnet  crossref  mathscinet  zmath  isi
    5. M. S. Bichegkuev, “Solvability conditions for the difference equations with an initial condition in a subspace”, Siberian Math. J., 51:4 (2010), 595–609  mathnet  crossref  mathscinet  isi  elib  elib
    6. Cai X., Huang J., Liu L., “Stability analysis of linear time-delay differential inclusion systems subject to input saturation”, Iet Control Theory and Applications, 4:11 (2010), 2592–2602  crossref  mathscinet  isi
    7. Bichegkuev M.S., “On some classes of infinitely differentiable operator semigroups”, Differ. Equ., 46:2 (2010), 224–238  crossref  mathscinet  zmath  isi  elib  scopus
    8. Cai X., Xu Sh., Wang X., Lv G., “Tracking Control of Linear Differential Inclusion Systems”, 2010 Etp/Iita Conference on System Science and Simulation in Engineering (Ssse 2010), ed. Tan H., Etp-Engineering Technology Press, 2010, 37–40  adsnasa  isi
    9. Huang J., Han Zh., Cai X., Liu L., “Robust Stabilization of Linear Differential Inclusions with Affine Uncertainty”, Circuits Syst. Signal Process., 30:6 (2011), 1369–1382  crossref  mathscinet  zmath  isi  elib  scopus
    10. Cai X., Huang J., Xie Q., “Output Tracking and Disturbance Rejection of Linear Differential Inclusion Systems”, Int. J. Syst. Sci., 43:11 (2012), 2072–2078  crossref  mathscinet  zmath  isi  elib  scopus
    11. V. B. Didenko, “On the continuous invertibility and the Fredholm property of differential operators with multi-valued impulse effects”, Izv. Math., 77:1 (2013), 3–19  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. A. G. Baskakov, “Analysis of linear differential equations by methods of the spectral theory of difference operators and linear relations”, Russian Math. Surveys, 68:1 (2013), 69–116  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    13. Cai X., Lin Yu., Hong Sh., “Stabilisation for One-Sided Lipschitz Non-Linear Differential Inclusions”, IET Contr. Theory Appl., 7:18 (2013), 2172–2177  crossref  mathscinet  zmath  isi  scopus
    14. V. M. Bruk, “Dissipative expansions of a symmetric relation generated by a system of integral equations with operator measures”, Russian Math. (Iz. VUZ), 58:12 (2014), 7–22  mathnet  crossref
    15. Cai X., Gao H., Liu L., Zhang W., “Control Design For One-Sided Lipschitz Nonlinear Differential Inclusions”, ISA Trans., 53:2 (2014), 298–304  crossref  isi  scopus
    16. Bichegkuev M.S., “Spectral Analysis of Differential Operators With Unbounded Operator Coefficients on the Half-Line”, Differ. Equ., 51:4 (2015), 431–439  crossref  mathscinet  zmath  isi  elib  scopus
    17. Ammar A., Jeribi A., Saadaoui B., “Frobenius–Schur Factorization for Multivalued
      $${\varvec{2\times 2}}$$
      2 2 Matrices Linear Operator”, Mediterr. J. Math., 14:1 (2017), UNSP 29  crossref  mathscinet  isi  elib  scopus
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