Periodic solutions of delay equations with several fixed delays (Q637021)

The problem on the existence and stability of a periodic solution of first-order differential delay equations is considered, where the non-linearities on the right-hand side are close to two-valued step functions. The author derives sufficient conditions under which the existence of periodic solutions of the problem with step functions on the right-hand side implies the existence as well as stability of similar periodic solutions of the original problem. The main results are proved by using fixed-point index arguments. Two illustrative examples are presented.