Proof and Generalization of Kaplan-Yorke's Conjecture on Periodic Solution of Differential Delay Equations
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In this paper, using the theory of existence of periodic solutions of Hamiltonian systems, we show that infinitely many periodic solutions of differential delay equations can be yielded from a family of periodic solutions of the coupled generalized Hamiltonian systems. Some sufficient conditions on the existence of periodic solutions of differential delay equations are obtained. As a corollary of our results, we show that the conjecture of Kaplan-Yorke on the search for periodic solutions for certain special classes of scalar differential delay equations is true.