关于Duffing方程周期解的一个基本定理的简化证明

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A Simplified Proof to a Theorem by DINH Tongren on Periodic Solutions of Duffing Equations

1.
Department of Mathematics, Nanjing Normal University, Nanjing 210097, P R China;
2.
Nankai Institute of Mathematics, Nankai University, Tianjin 300071, P R China

摘要: 1982年,关于带有双侧共振的Duffing方程周期解的存在性问题,丁同仁采用像平面分析法给出了一个基本定理。该文使用Leray-Schauder延拖原理给出一个简化证明。
- 周期解 /
- Duffing方程 /
- Leray-Schauder延拖原理
Abstract: In 1982, DING Tongren gave a basic theorem about existence of periodic solutions of Duffing equations with double resonance. A simplified proof will be given by making use of the Leray-Schauder principle.
- periodic solutions /
- Duffing equations /
- Leray-Schauder principle

[1]	DING Tong-ren. Nonlinear oscillations at a point of resonance[J]. Science of China Section A,1982,12(1):1-13.
[2]	Habets P, Metzen G. Existence of periodic solutions of Duffing equations[J]. J Differential Equations,1989,78(1):1-32.
[3]	Asakawa H. Landesman-Lazer type problems for Fucik spectrum[J]. Nonlinear Anal,1996,26(3):407-414.