International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 2, Pages 305-309
doi:10.1155/S0161171282000283

On the periodic solutions of linear homogeneous systems of differential equations

Abstract

Given a fundamental matrix ϕ(x) of an n-th order system of linear homogeneous differential equations Y′=A(x)Y, a necessary and sufficient condition for the existence of a k-dimensional (k≤n) periodic sub-space (of period T) of the solution space of the above system is obtained in terms of the rank of the scalar matrix ϕ(t)−ϕ(0).