Asymptotic integration of a system of differential equations with high-frequency terms in the critical case
- 63 Downloads
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.
Unable to display preview. Download preview PDF.
- 2.Vishik, M.I. and Lyusternik, L.A., Solutions of Some Problems on the Perturbation in the Case of Matrices and Self-Adjoint and Nonself-Adjoint Differential Equations, Uspekhi Mat. Nauk, 1960, vol. 15, no. 3 (93), pp. 3–80.Google Scholar
- 3.Shtokalo, I.Z., Lineinye differentsial’nye uravneniya s peremennymi koeffitsientami (Linear Differential Equations with Variable Coefficients), Kiev, 1960.Google Scholar
- 4.Levenshtam, V.B., Differentsial’nye uravneniya s bol’shimi vysokochastotnymi slagaemymi (Differential Equations with Large High-Frequency Terms), Rostov-on-Don, 2009.Google Scholar