International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 2, Pages 305-309

On the periodic solutions of linear homogenous systems of differential equations

A. K. Bose

Department of Mathematical Sciences, Clemson University, Clemson 29613, South Carolina, USA

Received 13 October 1981

Copyright © 1982 A. K. Bose. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 (kn) 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).