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The existence of periodic solutions for a class of functional differential equations and their application. (English) Zbl 0793.34054
Summary: Four sufficiency theorems of existence of periodic solutions for a class of retarded functional differential equations are given. The result of these theorems is better than the well-known Yoshizawa’s periodic solution theorem. An example of application is given at the end.
MSC:
34K99Functional-differential equations
34C25Periodic solutions of ODE
References:
[1]Yoshizawa, T., Stability theory by Liapunov’s second method,Math. Soc. Japan, Tokyo, (1966).
[2]Burton, T. A.,Volterra Integral and Differential Equations, Academic Press, New York, (1983), 286–287.
[3]Li Xiao-ying, On the generalization of Massera’s and Yoshizawa’s theorems for periodic solutions,Journal of Northeast Normal University,1 (1987), 11–16.
[4]Hale, J. K. and O. Lopes, Fixed point theorems and dissipative processes,J. Differential Equations,13 (1973), 391–402. · Zbl 0256.34069 · doi:10.1016/0022-0396(73)90025-9
[5]Zhao Jie-min, On the periodic solution problems of nonautonomous discret, periodic systems,Journal of Mathematical Research and Exposition,12, 3 (1992), 427-432.
[6]Burton, T. A.,Stability and Periodic Solutions of Ordinary and Functional Differential Equations, Academic Press, (1985), 246–251.