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

Jibin Li*, Xuezhong He

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

50 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)957-964
Number of pages8
JournalScience in China, Series A: Mathematics, Physics, Astronomy
Volume42
Issue number9
DOIs
Publication statusPublished - Sept 1999
Externally publishedYes

Keywords

  • Conjecture of Kaplan-Yorke
  • Differential-delay equations
  • Hamiltonian systems
  • Periodic solutions

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