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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2011, Volume 51, Number 6, Pages 1043–1055 (Mi zvmmf9462)  
This article is cited in 9 scientific papers (total in 9 papers)

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

Do Ngoc Thanha, V. B. Levenshtamab

a Department of Mathematics, Mechanics, and Computer Science, Southern Federal University, ul. Mil'chakova 8a, Rostov-on-Don, 344090 Russia
b Southern Institute of Mathematics, Vladikavkaz Scientific Center, Russian Academy of Sciences, ul. Markusa 22, Vladikavkaz, 362027 Russia
Full-text PDF (855 kB) Citations (9)
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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.
Key words: linear normal system with rapidly oscillating coefficients, degenerate stationary averaged system, complete asymptotic expansion of a periodic solution, Lyapunov stability and instability of a solution.
Received: 19.08.2010
English version:
Computational Mathematics and Mathematical Physics, 2011, Volume 51, Issue 6, Pages 975–986
DOI: https://doi.org/10.1134/S0965542511060042
Bibliographic databases:
Document Type: Article
UDC: 519.62
Language: Russian
Citation: Do Ngoc Thanh, V. B. Levenshtam, “Asymptotic integration of a system of differential equations with a large parameter in the critical case”, Zh. Vychisl. Mat. Mat. Fiz., 51:6 (2011), 1043–1055; Comput. Math. Math. Phys., 51:6 (2011), 975–986
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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