THE EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR SYSTEMS OF FIRST-ORDER DIFFERENTIAL EQUATIONS AT RESONANCE

Applied Mathematics and Mechanics (English Edition) ›› 2000, Vol. 21 ›› Issue (11): 1282-1291.

THE EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR SYSTEMS OF FIRST-ORDER DIFFERENTIAL EQUATIONS AT RESONANCE

马世旺^1,2, 王志成², 庾建设²

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

收稿日期:1998-03-25 修回日期:2000-04-12 出版日期:2000-11-18 发布日期:2000-11-18
基金资助:
the National Natural Science Foundation of China(19801014;19971026;19831030)

THE EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR SYSTEMS OF FIRST-ORDER DIFFERENTIAL EQUATIONS AT RESONANCE

MA Shi-wang^1,2, WANG Zhi-cheng², YU Jian-she²

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

Received:1998-03-25 Revised:2000-04-12 Online:2000-11-18 Published:2000-11-18
Supported by:
the National Natural Science Foundation of China(19801014;19971026;19831030)

摘要/Abstract

摘要： 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 co incidence degree are obtained.Some applications of the main results to Duffing's equations are also given.

中图分类号:

O175

马世旺;王志成;庾建设. THE EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR SYSTEMS OF FIRST-ORDER DIFFERENTIAL EQUATIONS AT RESONANCE[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(11): 1282-1291.

MA Shi-wang;WANG Zhi-cheng;YU Jian-she. THE EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR SYSTEMS OF FIRST-ORDER DIFFERENTIAL EQUATIONS AT RESONANCE[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(11): 1282-1291.

参考文献

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THE EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR SYSTEMS OF FIRST-ORDER DIFFERENTIAL EQUATIONS AT RESONANCE

THE EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR SYSTEMS OF FIRST-ORDER DIFFERENTIAL EQUATIONS AT RESONANCE

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