On Existence Of Two Real Periodic Solutions Of Differential Equations Of Riccati Type

Abstract

In this paper we consider the two equations z^z^p^z+r^t), (*) z^z^ptOz+r^t), (••) where z € C, p, r) and r^ are real, continuous and periodic with period T. It was shown in[2]that if (*) has two T-periodic solutions and if r j (t) < ty (t) for all t£ [ 0, T ], then (**) has two T-periodic solutions. In this note we extend this result by showing that if, moreover, the two T-periodic solutions of (*) are real then so are the T-periodic solutions of( **).