Geodesic
Asymptotic integration of a system of differential equations with a large parameter in the critical case
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 6, pp. 1043-1055

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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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     title = {Asymptotic integration of a~system of differential equations with a~large parameter in the critical case},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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Do Ngoc Thanh; V. B. Levenshtam. Asymptotic integration of a system of differential equations with a large parameter in the critical case. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 6, pp. 1043-1055. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a6/