On Periodic Solutions of Degenerate Singularly Perturbed Linear Systems with Multiple Elementary Divisor

We establish sufficient conditions for the existence and uniqueness of a periodic solution of a system of linear differential equations with a small parameter and a degenerate matrix of coefficients of derivatives in the case of a multiple spectrum of a boundary matrix pencil. We construct asymptotics of this solution.     

On the Existence and Asymptotics of a Periodic Solution of a Degenerate Singularly Perturbed System of Differential Equations in the Case of Multiple Elementary Divisors

We consider a linear inhomogeneous singularly perturbed system of differential equations with -periodic coefficients and identically degenerate matrix with the derivative. We establish sufficient conditions for the existence and uniqueness of an -periodic solution of this system in the case where the main pencil of matrices has multiple spectrum. We construct asymptotics of this solution.     

Stability of Solutions of a Degenerate Linear System of Differential Equations

We introduce the concept of stability of solutions of a system of linear differential equations with an identically degenerate matrix as the coefficient of the derivative. We find necessary and sufficient conditions for the stability of such systems. We generalize the Floquet–Lyapunov theory to systems of this type with periodic coefficients.