| 具时滞的高维周期系统周期解的存在性与唯一性 |
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| 引用本文： | 曹进德,李永昆. 具时滞的高维周期系统周期解的存在性与唯一性[J]. 数学学报, 1997, 40(2): 280-286. DOI: cnki:ISSN:0583-1431.0.1997-02-016 |
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| 作者姓名： | 曹进德 李永昆 |
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| 作者单位： | 云南大学成人教育学院 昆明650091(曹进德)，云南大学数学系 昆明650091(李永昆) |
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| 摘 要： | 本文考虑了具时滞的高维周期系统x’(t)=A(t,x(t))x(t)+f(t,x(t-r)),其中(t,x)∈R×R~n,A(t,x)是n×n连续矩阵,f(t,x)是n维连续向量,且A(t+T,x)=A(T,x),f(t十T,x)=f(t,x).利用不动点方法,建立了保证其T周期解的存在性及唯一性的充分条件.所得结果推广、改进了文[1-3]的主要结果.
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| 关 键 词： | 时滞 周期解 存在性 唯一性 |
| 收稿时间： | 1994-12-16 |
| 修稿时间： | 1996-04-11 |
The Existence and Uniqueness of Periodic Solutions to Higher Dimensional Periodic System with Delay |
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| Cao Jinde. The Existence and Uniqueness of Periodic Solutions to Higher Dimensional Periodic System with Delay[J]. Acta Mathematica Sinica, 1997, 40(2): 280-286. DOI: cnki:ISSN:0583-1431.0.1997-02-016 |
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| Authors: | Cao Jinde |
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| Affiliation: | Cao Jinde (Adult Education College, Vunnan University, Kunming 650091, China)Li Yongkun (Department of Mathematics, yunnon University, Kunming 650091, China) |
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| Abstract: | In this paper, higher dimensional periodic systems with delay of the form x'(t) = A(t,x(t))x(t) + f(t,x(t - r)) are considered, where the n x n matrix A(t, x) and the n-vector f(t,x) are continuous in (t,x) ∈ R × Rn, and A(t + T,x)-A(t,x), f(t + T, x) = f(t, x). Using fixed point method, some sufficient conditions to guarantee the existence and uniqueness of T periodic solution for the systems are obtained. The main results in [1-3] are extended and improved. |
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| Keywords: | Delay Periodic solution Existence Uniqueness |
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