一类向量Liénard方程的概周期解的存在性  

Almost Periodic Solutions for a Class of Forced Liénard Equations

作　　者：李丽洁[1] 杨启贵[2] 

机构地区：[1]广西师范大学数学科学学院,桂林541004 [2]华南理工大学数学科学学院,广州510640

出　　处：《工程数学学报》2008年第4期672-678,共7页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10461002);广东省自然科学基金(05300162)

摘　　要：本文讨论了一类带概周期强迫项向量Liénard方程的概周期解的存在性。以次变泛函代替范数推广最小解的概念,结合概周期系统的壳理论,在一定条件下通过证明次变泛函最小解的唯一性得到方程至少存在一个概周期解的充分条件,并证明了方程的有界解均为概周期解。最后给出主要定理的一个应用实例。所得结果推广了文献中的部分工作。This paper investigates the existence of almost periodic solutions for a class of forced vectorial Liénard equations. We construct a suitable subvariant function which in some sense is a generalization of the idea of minimizing the norm. Furthermore, by using the almost periodic functional hull theory, we show that there is an unique minimum of the subvariant function over solutions of equation. Therefore, we obtain that the system admits at most one almost periodic solution. Besides we state that all bounded solutions are almost periodic. Finally, an example illustrates the main theoretical result. Our conclusions are the natural generalization of the related results.

关 键 词：向量Liénard方程 最小解 概周期解 

分 类 号：O174.14[理学—数学]