Periodic solutions of systems of differential equations
Irving J. Epstein · Proceedings of the American Mathematical Society · 1962
where 2 is skew symmetric and periodic with period c. If z is also odd, (Z(t) = -2( -t)), Demidovic [I ] has shown that Y will be periodic. We give below a simple proof of this result, in which moreover the hypothesis that the matrix be skew symmetric is dropped. If z is not odd, nothing beyond the Floquet theory is known about the periodicity of Y. When z is a 3 X 3 matrix we shall use a theorem in differential geometry, which is due to Fenchel [2], to obtain a necessary condition on the elements of 2, in order that Y be periodic with period w.