在共振点的一阶微分系统的周期解

马世旺; 王志成; 庾建设

在共振点的一阶微分系统的周期解

1.
上海交通大学应用数学系, 上海 200030;
2.
湖南大学应用数学系, 长沙 410082

基金项目: 国家自然科学基金资助项目(19801014;19971026;19831030)

详细信息

作者简介:
马世旺(1965- ),男,内蒙古人,副教授,博士.

中图分类号: O175
计量
- 文章访问数: 2422
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- 被引次数: 0
出版历程
- 收稿日期: 1998-03-25
- 修回日期: 2000-04-12
- 刊出日期: 2000-11-15

The Existence of Periodic Solutions for Nonlinear Systems of First-Order Differential Equations at Resonance

1.
Department of Applied Mathematics, Shanghai Jiaotong University, Shanghai 200030, P R China;
2.
Department of Applied Mathematics, Hunan University, Changsha, Hunan 410082, P R China

摘要

摘要: 考虑具偏差变元的一阶非线性微分系统:x>(t)=Bx(t)+F(x(t-τ))+p(t),其中,x(t)∈R²,τ∈R,B∈R^2×2,F是有界的,p(t)是连续的2π-周期函数.应用Brouwer度及Mawhin重合度理论,在共振的情况下,给出了上述方程存在2π-周期解的充分条件及其在Duffing方程上的应用.
- 一阶微分方程 /
- 周期解 /
- 共振 /
- Brouwer度 /
- 重合度 /
- Duffing方程
Abstract: The nonlinear system of first-order differential equations with a deviating argument x>(t)=Bx(t)+F(x(t-τ))+p(t),is considered,where x(t)∈R²,τ∈R,B∈R^2×2 F is bounded and p(t) is continuous and 2π-periodic.Some sufficient conditions for the existence of 2π-periodic solutions of the above equation,in a resonance case,by using the Brouwer degree theory and a continuation theorem based on Mawhin's coincidence degree are obtained.Some applications of the main results to Duffing's equations are also given.
- first-order differential equation /
- periodic solution /
- resonance /
- Brouwer degree /
- coincidence degree /
- Duffing equation

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参考文献(13)

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