A Criterion of Existence of a Periodic Solution for n-th Order Systemsof Autonomous Differential Equations (n\geq 3)
Citation：
Ye Dawei.A Criterion of Existence of a Periodic Solution for n-th Order Systemsof Autonomous Differential Equations (n\geq 3)[J].Chinese Annals of Mathematics B,1983,4(3):285~292
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Authors：
Ye Dawei;
Abstract：
There have been many results^[1-7] on seeking a periodic solution for systems of autonomous differential equations by using the torus principl. The finest one amony them is still Liapunov’s method of rotating functions proposed by В. B. Nemytskii[3’4]. However, this method is limited in the case that the absolute values of derivatives of rotating functions are greater than some positive constants. This paper summarizes the methods proposed in[3-5] and gives a more careful criterion such that derivatives of rotating functions might be alternative functions. The author provides a sufficient condition of existence of a periodic solution for systems of autonomous differential equations by Using Liapunov’s method of rotating functions under more general circumstances.
