Periodic Solutions of Linear and Quasilinear Neutral Functional Differential Equations

In this paper we will use the Fourier expansions to generalize Hale′s alternative results for the existence of periodic solutions of linear retarded functional differential equations to neutral equations. Using some a priori estimation and the Leray-Schauder degree theory, we will obtain some existence theorems of periodic solutions for a class of quasilinear neutral equations. The results also generalize the works of Hatvani and Krisztin on retarded equations.