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

34K99Functional-differential equations
34C25Periodic solutions of ODE
Full Text: DOI
[1] S. Chow, ”Existence of periodic solutions of autonomous functional differential equations,” to appear. · 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’$(x) = -{\alpha}$f (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’$(x) = -{\alpha}f(x - 1) [1 + f(x)]$. 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) · Zbl 0135.37001
[7] J. L. Kaplan and J. A. Yorke, On the stability of a periodic solution of a differential delay equation, SIAM J. Math. Anal., to appear. · Zbl 0241.34080
[8] Nussbaum, R. D.: Periodic solutions of some nonlinear autonomous functional differential equations. Ann. mat. Pura. appl. (1974) · 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