一类泛函微分方程周期解的存在性与应用
The Existence of Periodic Solutions for a Class of Functional Differential Equations and Their Application
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摘要: 本文给出了一类滞后型泛函微分方程有一个周期解的四个充分性定理,其结果明显地优于着名的Yoshizawa周期解定理,最后给出了应用实例。Abstract: In this paper,the retarded functional differential equation are considered, We obtain four existence theorems of periodc solutions of it, The application of these theorems are convenient and efficient and the theorem of this paper is better than the well-known Yoshizawa's periodic solution theorem.A feedback system is discussed in detail and a sufficient condition of guaranteeing the existence of an ω-Periodic motion of the system is got by applying these theorems in this paper.
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[1] Yoshizawa,T.,Stability theory by Liapunov's second method.Math.Soc.Japan,Tokyo,(1966). [2] Burton,T.A.,Volterra Integral anal Differential Equations,Academic Press,New York,(1983),286-287. [3] 李晓颖,关于Massera及Yoshizawa周期解定理的推广,东北师大学报自然科学版.1(1987),11-16 [4] Hale,J.K.and O.Lopes,Fixed point theorems and dissipative processes,J.Differential Equations,13(1973),391-402. [5] 赵杰民.关于非自治离散周期系统的周期解问题,数学研究与评论,(12) 3 (1992),427-432. [6] Burton, T,A,,Stability and Periodic Solutions of Ordinary and Functional Differentiol Equations, Academic Przss(1985), 246-251. -
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