Proof and Generalization of Kaplan-Yorke's Conjecture on Periodic Solution of Differential Delay Equations

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Li, Jibin
He, Xue-Zhong
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http://hdl.handle.net/1853/29550
Abstract
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.
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1994
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