, Volume 48, Issue 8, pp 1177-1179

Asymptotic integration of a system of differential equations with high-frequency terms in the critical case

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Abstract

We construct the complete asymptotics of a periodic solution of a linear normal system of differential equations with high-frequency coefficients. We study the Lyapunov stability and instability of that solution. More specifically, we consider the critical case in which the matrix coefficient of the formally averaged stationary system has one eigenvector and one generalized (in the Vishik-Lyusternik sense) associated vector.

Original Russian Text © N.T. Do, V.B. Levenshtam, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 8, pp. 1190–1192.