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Mat. Sb., 2001, Volume 192, Number 3, Pages 65–82 (Mi msb551)  

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

On some methods for investigating stability

Yu. A. Konyaev

Peoples Friendship University of Russia

Abstract: This article contains various algorithms for investigating the stability (using the apparatus of the splitting method) of certain classes of non-autonomous systems of linear and quasi-linear ordinary differential equations. The results complement previously known results. Each of the algorithms presented can be regarded (in a certain sense) as a development of the classical method of normal forms, which is very effective in the study of non-linear systems for analysing linear and quasi-linear non-autonomous systems of ordinary differential equations.

DOI: https://doi.org/10.4213/sm551

Full text: PDF file (261 kB)
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English version:
Sbornik: Mathematics, 2001, 192:3, 385–402

Bibliographic databases:

UDC: 925.51
MSC: Primary 34C20, 34D15; Secondary 34D05, 34B30, 34C15, 37C60, 70E05
Received: 25.08.1999 and 22.05.2000

Citation: Yu. A. Konyaev, “On some methods for investigating stability”, Mat. Sb., 192:3 (2001), 65–82; Sb. Math., 192:3 (2001), 385–402

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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. Yu. A. Konyaev, D. V. Mikhailov, V. B. Mergiya, “Analiz malykh kolebanii mikromekhanicheskogo giroskopa (MMG) na vibratsionnom osnovanii”, Matem. modelirovanie, 24:5 (2012), 61–64  mathnet  mathscinet
    2. Konyaev Yu.A., Fedorov Yu.S., Vorkne A.Z., “O kriteriyakh ustoichivosti resheniya singulyarno vozmuschennykh zadach dlya neavtonomnykh sistem obyknovennykh differentsialnykh uravnenii s periodicheskoi matritsei pri nalichii kratnogo spektra”, Vestnik moskovskogo energeticheskogo instituta, 2012, no. 6, 42–46  mathscinet  elib
    3. Khoa N.V., “Ob asimptoticheskoi privodimosti nekotorykh klassov modelnykh sistem obyknovennykh differentsialnykh uravnenii (odu) s kvazipolinomialnoi matritsei”, Vestnik rossiiskogo universiteta druzhby narodov. seriya: matematika, informatika, fizika, 2012, no. 2, 13–18  elib
    4. Konyaev Yu.A., Mergiya B.V., Khoa N.V., “O regulyarnykh i singulyarnykh vozmuschennykh modelnykh sistemakh odu polinomialnogo tipa s osobennostyami”, Vestnik rossiiskogo universiteta druzhby narodov. seriya: matematika, informatika, fizika, 2012, no. 3, 20–24  elib
    5. Konyaev Yu.A., Mikhailov D.V., Romanova E.Yu., “Asymptotic Analysis of a Model Gyro System”, Differ. Equ., 49:6 (2013), 760–764  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    6. A. G. Eliseev, Yu. A. Konyaev, D. A. Shaposhnikova, “Unique Solvability of Singularly Perturbed Boundary-Value Problems with Unstable Spectrum of the Limit Operator”, Math. Notes, 95:2 (2014), 204–207  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. Yu. A. Konyaev, D. A. Maslov, “Specific Features of the Study of Nonautonomous Differential Equations with Exponential-Type Matrices”, Math. Notes, 101:2 (2017), 260–264  mathnet  crossref  crossref  mathscinet  isi  elib
    8. Yu. A. Konyaev, D. A. Maslov, “Analysis of nonautonomous systems of ordinary differential equations with exponentially periodic matrix”, Russian Math. (Iz. VUZ), 61:10 (2017), 54–60  mathnet  crossref  isi
    9. Yu. A. Konyaev, D. A. Maslov, “An Asymptotic Method for Reducing Systems of Differential Equations with Almost-Periodic Matrices”, Math. Notes, 105:1 (2019), 8–15  mathnet  crossref  crossref  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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