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

MA Shi-wang; WANG Zhi-cheng; YU Jian-she

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Article Navigation > Applied Mathematics and Mechanics > 2000 > 21(11): 1156-1164

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, 2000, 21(11): 1156-1164.

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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

Received Date: 1998-03-25
Rev Recd Date: 2000-04-12
Publish Date: 2000-11-15

Abstract

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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References(13)

References

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