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Periodic solutions of some differential delay equations created by Hamiltonian systems

  • Jibin Li (a1), Zhengrong Liu (a2) and Xuezhong He (a3)
Abstract

This paper is concerned with finding periodic solutions of differential delay systems

and

where ri (i = 1, 2,…, n − 1) are positive constants. By using the theory of Hamiltonian systems, we obtain some sufficient conditions under which these systems have many periodic solutions with known periods.

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[2]O. Arino and A.A. Cherif , ‘More on ordinary differential equations which yield periodic solutions of delay differential equations’, J. Math. Anal. Appl. 180 (1993), 361385.

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[5]P. Dormayer , ‘Exact formulae for periodic solutions of x(t + 1) = α(−x(t) + x3(t))’, Z. Angew. Math. Phys. 37 (1986), 765775.

[9]K. Gopalsamy , J. Li and X. He , ‘On the construction of periodic solutions of Kaplan-Yorke type for some differential delay equations’, Appl. Anal. 59 (1995), 6580.

[10]A.V. Herz , ‘Solution of x(t) = −g(x(t − 1)) approach the Kaplan-Yorke orbits for odd sigmoid’, J. Differential Equations 118 (1995), 3653.

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[14]R.D. Nussbaum , ‘Uniqueness and onouniqueness for periodic solutions x′(t) = −g(x(t − 1))’, J. Differential Equations 34 (1979), 2554.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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