Proof and generalization of Kaplan-Yorke's conjecture under the condition f ' (0) > 0 on periodic solution of differential delay equations

Using the theory of existence of periodic solutions of Hamiltonian systems, it is shown that many periodic solutions of differential delay equations c an be yielded from many families of periodic solutions of the coupled gener alized Hamiltonian systems. Some sufficient conditions on the existence of periodic solutions of differential delay equations are obtained. As a corol lary of our results, the conjecture of Kaplan-Yorke on the search for perio dic solutions for certain special classes of scaler differential delay equa tions is shown to be true when f' (0) = omega > 0.