DIFFERENTIAL PERIODIC RICCATI-EQUATIONS - A NOTE ON THE EXISTENCE OF AN INFINITE NUMBER OF PERIODIC STRONG SOLUTIONS

The differential matrix Riccati equation with periodic coefficients is considered. It is shown by means of a counter-example that a sufficient condition for the existence of an infinite number of periodic non-negative definite solutions given in a previous paper is not appropriately stated. A suitable adjustment of the assumptions allows one to work out rigorous sufficient conditions. Thanks to these results, a necessary and sufficient condition for the existence of the periodic strong solution, which relied on the incorrect condition, can be shown to be still valid.