＜正＞ There have been many results on seeking a periodic solution for systems ofautonomous differential equations by using the terns principl.The finest one amony them isstill Liapunov’s method of rotating functions proposed by B.B.Nemytskii.However,this method is limited in the case that the absolute values of derivatives of rotating functionsare greater than some positive constants.This paper summarizes the methods proposedin[3-5] and gives a more careful criterion such that derivatives of rotating functionsmight be alternative functions.The author provides a sufficient condition of existence ofa periodic solution for systems of autonomous differential equations by using Liapunov’smethod of rotating functions under more general circumstances.
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