Periodic solutions of some differential delay equations created by Hamiltonian systems

Bulletin of the Australian Mathematical Society

Volumn 60, Issue 3, 1999, Pages 377-390

  Li, Jibin ^a   Liu, Zhengrong ^b   He, Xuezhong ^c  

^a KUNMING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b YUNNAN UNIVERSITY   (China)

^c UNIVERSITY OF SYDNEY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040036791     PISSN: 00049727     EISSN: None     Source Type: Journal    
DOI: 10.1017/s000497270003656x     Document Type: Article

References (16)

1. O. Arino and A.A. Cherif, 'An exact formula for the branch of period-4-solutions of ẋ = -λf(x(t - 1)) which bifurcates at λ = π/2', Differential Integral Equations 2 (1989), 162-169.
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), 361-385.
3. Y. Chen, 'The existence of periodic solutions of the equation x′(t) = -f(x(t), x(t - τ))', J. Math. Anal. Appl. 163 (1992), 227-237.
4. Y. Chen, 'The existence of periodic solutions for a class of neutral differential difference equations', J. Austral. Math. Soc. Ser. B 33 (1992), 508-516.
5. 3(t))', Z. Angew. Math. Phys. 37 (1986), 765-775.
6. W. Ge, 'The number of simple periodic solutions to the differential-difference equation ẋ(t) = f(x(t - 1))', Chinese Ann. Math. Ser. A 14 (1993), 472-479.
7. W. Ge, 'Periodic solutions of differential delay equations with multiple lags', Acta. Math. Appl. Sinica 17 (1994), 172-181.
8. s with multiple lags', Acta. Math. Sinica (to appear).
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), 65-80.
10. A.V. Herz, 'Solution of ẋ(t) = -g(x(t - 1)) approach the Kaplan-Yorke orbits for odd sigmoid', J. Differential Equations 118 (1995), 36-53.
11. J.L. Kaplan and J.A. Yorke, 'Ordinary differential equations which yield periodic solutions of differential-delay equations', J. Math. Anal. Appl. 48 (1974), 317-324.
12. J. Li and X. He, 'Proof and generalisation of Kaplan-Yorke's conjecture on periodic solution of differential delay equations', Sci. Sinica Ser. A 47 (1999), 1-9.
13. R.D. Nussbaum, 'Periodic solutions of special differential equation: an example in nonlinear functional analysis', Proc. Royal. Soc. Edinburgh Sect. A 81 (1978), 131-151.
14. R.D. Nussbaum, 'Uniqueness and onouniqueness for periodic solutions x′(t) = -g(x(t - 1))', J. Differential Equations 34 (1979), 25-54.
15. L. Wen, 'Existence of periodic solutions of a class of differential-difference equations', Chinese Ann. Math. Ser. A 10 (1989), 249-254.
16. L. Wen and H. Xia, 'Existence of periodic solutions for differential-difference equation with two time laps', Sci. Sinica Ser. A 31 (1988), 777-786.