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.