Coincidence degree and periodic solutions of neutral equations

A study is made of the problem of existence of periodic solutions for some nonautonomous neutral functional differential equations. It is essentially an application of a basic theorem on the Fredholm alternative for periodic solutions of some linear neutral equations recently obtained by Hale (1973) and of a generalized Leray-Schauder theory developed by Mawhin (1972, and to appear). Although their proofs are surprisingly simple, the obtained results are nontrivial extensions to the neutral case of a number of recent existence theorems for periodic solutions of functional differential equations.