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Ordinary differential equations which yield periodic solutions of differential delay equations. (English) Zbl 0293.34102


MSC:

34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34C25 Periodic solutions to ordinary differential equations
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References:

[1] S. Chow; S. Chow · Zbl 0295.34055
[2] Grafton, R. B., A periodicity theorem for autonomous functional differential equations, J. Differential Equations, 6, 87-109 (1969) · Zbl 0175.38503
[3] Grafton, R. B., Periodic solutions of certain Liénard equations with delay, J. Differential Equations, 11, 519-527 (1972) · Zbl 0231.34063
[4] Jones, G. S., The existence of periodic solutions of \(f\)′\((x)\) = −\( αf (x\) − 1)\([1 + f(x)]\), J. Math. Anal. Appl., 5, 435-450 (1962) · Zbl 0106.29504
[5] Jones, G. S., On the nonlinear differential difference equation \(f\)′\((x)\) = −\( αf (x\) − 1) \([1 + f(x)]\), J. Math. Anal. Appl., 4, 440-469 (1962) · Zbl 0106.29503
[6] Jones, G. S., Periodic motions in Banach space and applications to functional differential equations, Contrib. Differential Equations, 3, 75-106 (1964)
[7] J. L. Kaplan and J. A. YorkeSIAM J. Math. Anal.; J. L. Kaplan and J. A. YorkeSIAM J. Math. Anal. · Zbl 0241.34080
[8] Nussbaum, R. D., Periodic solutions of some nonlinear autonomous functional differential equations, Ann. Mat. Pura. Appl. (1974), to appear · Zbl 0323.34061
[9] Nussbaum, R. D., Periodic solutions of some nonlinear, autonomous functional differential equations. II, J. Differential Equations, 14, 360-394 (1973) · Zbl 0311.34087
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