On the periodic solutions of linear homogenous 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).

Keywords

• linear homogeneous system of differential equations
• fundamental matrix
• periodic solutions
• periodic sub-spaces of (period T)
• rank of the scalar matrix
• linearly independent vectors.