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Sibirsk. Mat. Zh., 2004, Volume 45, Number 6, Pages 1271–1284 (Mi smj1138)  

This article is cited in 14 scientific papers (total in 14 papers)

On stability of solutions to quasilinear periodic systems of differential equations

G. V. Demidenko, I. I. Matveeva

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We consider a quasilinear system of differential equations with periodic coefficients in the linear terms. We obtain estimates for the attraction domain of the zero solution and establish estimates for the decay rate of solutions at infinity. The results are stated in terms of the integrals of the norm of a periodic solution to the Lyapunov differential equation.

Keywords: asymptotic stability, attraction domain, Lyapunov differential equation

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English version:
Siberian Mathematical Journal, 2004, 45:6, 1041–1052

Bibliographic databases:

UDC: 517.925.51
Received: 17.04.2003

Citation: G. V. Demidenko, I. I. Matveeva, “On stability of solutions to quasilinear periodic systems of differential equations”, Sibirsk. Mat. Zh., 45:6 (2004), 1271–1284; Siberian Math. J., 45:6 (2004), 1041–1052

Citation in format AMSBIB
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\by G.~V.~Demidenko, I.~I.~Matveeva
\paper On stability of solutions to quasilinear periodic systems of differential equations
\jour Sibirsk. Mat. Zh.
\yr 2004
\vol 45
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\pages 1271--1284
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\zmath{https://zbmath.org/?q=an:1105.34033}
\transl
\jour Siberian Math. J.
\yr 2004
\vol 45
\issue 6
\pages 1041--1052
\crossref{https://doi.org/10.1023/B:SIMJ.0000048919.83985.25}
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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. K. Aidyn, H. Ya. Bulgakov, G. V. Demidenko, “An estimate for the attraction domains of difference equations with periodic linear terms”, Siberian Math. J., 45:6 (2004), 983–991  mathnet  crossref  mathscinet  zmath  isi
    2. Yu. Yu. Klevtsova, “O chislennom issledovanii asimptoticheskoi ustoichivosti reshenii lineinykh sistem s periodicheskimi koeffitsientami”, Sib. zhurn. industr. matem., 8:2 (2005), 103–115  mathnet  mathscinet
    3. G. V. Demidenko, I. I. Matveeva, “Asimptoticheskie svoistva reshenii differentsialnykh uravnenii s zapazdyvayuschim argumentom”, Vestn. NGU. Ser. matem., mekh., inform., 5:3 (2005), 20–28  mathnet
    4. I. I. Matveeva, E. A. Samuilova, “Approximate solution of a boundary value problem for the Lyapunov differential equation with a parameter”, J. Appl. Industr. Math., 2:2 (2008), 222–230  mathnet  crossref  mathscinet
    5. I. I. Klevtsova, “An algorithm for the numerical investigation of the asymptotic stability of solutions of linear systems with periodic coefficients”, J. Appl. Industr. Math., 3:2 (2009), 234–245  mathnet  crossref  mathscinet
    6. G. V. Demidenko, I. I. Matveeva, “Stability of solutions to delay differential equations with periodic coefficients of linear terms”, Siberian Math. J., 48:5 (2007), 824–836  mathnet  crossref  mathscinet  zmath  isi
    7. Yu. Yu. Klevtsova, “Ob odnoi kharakteristike asimptoticheskoi ustoichivosti reshenii lineinykh sistem s periodicheskimi koeffitsientami”, Vestn. NGU. Ser. matem., mekh., inform., 8:3 (2008), 60–80  mathnet
    8. Matveeva I.I., Balakina E.Yu., Dulina K.M., “Ob asimptoticheskoi ustoichivosti reshenii odnogo klassa sistem differentsialnykh uravnenii s neskolkimi zapazdyvaniyami”, Vestnik Tambovskogo universiteta. Seriya: Estestvennye i tekhnicheskie nauki, 16:5 (2011), 1260–1263  elib
    9. Matveeva I.I., Scheglova A.A., “Otsenki reshenii odnogo klassa nelineinykh differentsialnykh uravnenii s zapazdyvayuschim argumentom s parametrami”, Matematicheskie zametki YaGU, 19:1 (2012), 60–69  mathscinet  zmath  elib
    10. G. V. Demidenko, K. M. Dulina, I. I. Matveeva, “Asimptoticheskaya ustoichivost reshenii odnogo klassa nelineinykh differentsialnykh uravnenii vtorogo poryadka s parametrami”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 14, 39–52  mathnet
    11. G. V. Demidenko, “Systems of differential equations with periodic coefficients”, J. Appl. Industr. Math., 8:1 (2014), 20–27  mathnet  crossref  mathscinet
    12. M. A. Skvortsova, “Asymptotic properties of solutions to a system describing the spread of avian influenza”, Sib. elektron. matem. izv., 13 (2016), 782–798  mathnet  crossref
    13. G. V. Demidenko, A. A. Bondar, “Exponential dichotomy of systems of linear difference equations with periodic coefficients”, Siberian Math. J., 57:6 (2016), 969–980  mathnet  crossref  crossref  isi  elib
    14. G. V. Demidenko, A. V. Dulepova, “On stability of the inverted pendulum motion with a vibrating suspension point”, J. Appl. Industr. Math., 12:4 (2018), 607–618  mathnet  crossref  crossref
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