On the periodic solutions of linear homogenous systems of differential equations

[摘要] Given a fundamental matrixϕ(x)of ann-th order system of linear homogeneous differential equationsY′=A(x)Y, a necessary and sufficient condition for the existence of ak-dimensional(k≤n)periodic sub-space (of periodT) of the solution space of the above system is obtained in terms of the rank of the scalar matrixϕ(t)−ϕ(0).

[学科分类] 数学（综合）