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Asymptotic integration of a system of differential equations with a large parameter in the critical case

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Abstract

For a linear normal system of ordinary differential equations with rapidly oscillating coefficients in a critical case, the existence of a unique periodic solution is proved, its complete asymptotic expansion is constructed and justified, and Lyapunov stability and instability conditions are found. The asymptotic series constructed is shown to converge absolutely and uniformly to the solution.

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Authors and Affiliations

  1. Department of Mathematics, Mechanics, and Computer Science, Southern Federal University, ul. Mil’chakova 8a, Rostov-on-Don, 344090, Russia

    Ngoc Thanh Do & V. B. Levenshtam

  2. Southern Institute of Mathematics, Vladikavkaz Scientific Center, Russian Academy of Sciences, ul. Markusa 22, Vladikavkaz, 362027, Russia

    V. B. Levenshtam

Authors
  1. Ngoc Thanh Do
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  2. V. B. Levenshtam
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Correspondence to Ngoc Thanh Do.

Additional information

Original Russian Text © Ngoc Thanh Do, V.B. Levenshtam, 2011, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 6, pp. 1043–1055.

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Do, N.T., Levenshtam, V.B. Asymptotic integration of a system of differential equations with a large parameter in the critical case. Comput. Math. and Math. Phys. 51, 975–986 (2011). https://doi.org/10.1134/S0965542511060042

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  • DOI: https://doi.org/10.1134/S0965542511060042

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