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

作　　者：李继彬 何学忠 

出　　处：《Science China Mathematics》1999年第9期957-964,共8页中国科学：数学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant No. 19731003);Science Foundation of Yunnan Province.

摘　　要：Using the theory of existence of periodic solutions of Hamiltonian systems, it is shown that many periodic solutions of differential delay equations can be yielded from many families 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, the conjecture of Kaplan-Yorke on the search for periodic solutions for certain special classes of scalar differential delay equations is shown to be true when f' (0) =ω> 0.Using the theory of existence of periodic solutions of Hamiltonian systems, it is shown that many periodic solutions of differential delay equations can be yielded from many families 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, the conjecture of Kaplan-Yorke on the search for periodic solutions for certain special classes of scalar differential delay equations is shown to be true when f’(0)=ω>0.

关 键 词：differential-delay equations HAMILTONIAN systems periodic solutions CONJECTURE of Kaplan-Yorke. 

分 类 号：O175[理学—数学]