摘要
本文利用Ｌｉａｐｕｎｏｖ函数讨论了非线性概周期系统的概周期解的存在性，所得结果推广了文［３］和［４］的一些著名结果．
In this paper, we show following theorem: Theorem . Let K SB be a compact set. The system x=f(t ,x) (1) has a bounded solution Φ(t) ∈ K for t∈R,If there exists a Liapunov function V(t ,x) difined on R × SB which is unifomly continuous and satisfies i) |V (t,x)|≤a(||x-Φ(t)||);. Then system (1) has unique almost periodic solution P(t) in SB with mod where a (r) and b(r) are continuous , increase and positive functions with a (0) = b(0) = 0.
出处
《晓庄学院自然科学学报》
CAS
1995年第2期4-8,共5页
Journal of Natural Science of Hunan Normal University
基金
国家自然科学基金
关键词
李雅普诺夫函数
非线性
概周期解
紧集
Liapunov function
nonlinear almost periodic differential equation
almost periodic solution
compact set
