Conditionally periodic solutions of the canonical systems of differential equations in non-autonomous resonant case

1979 ◽  
Vol 19 (1) ◽  
pp. 77-93 ◽  
Author(s):  
S. G. Zhuravlev
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Canonical Systems ◽  
Resonant Case ◽  
Systems Of Differential Equations

scholarly journals On the periodic solutions of linear homogenous systems of differential equations

1982 ◽  
Vol 5 (2) ◽  
pp. 305-309
Author(s):  
A. K. Bose
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Fundamental Matrix ◽  
Solution Space ◽  
Order System ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Scalar Matrix ◽  
Systems Of Differential Equations ◽  
Necessary And Sufficient

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).

Sign in / Sign up

Export Citation Format

Share Document