BASED on the Nussbaum’s results, we studied in ref. [2] the conditions for the existence of oscillatory periodic solutions to the differential-delay equations (DDEs)
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 coupl...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.展开更多
文摘BASED on the Nussbaum’s results, we studied in ref. [2] the conditions for the existence of oscillatory periodic solutions to the differential-delay equations (DDEs)
基金Project supported by the National Natural Science Foundation of China (Grant No. 19731003)Science Foundation of Yunnan Province.
文摘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.
