| Duffing方程的奇异点方法 |
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| 引用本文： | 陈红斌,李开泰. Duffing方程的奇异点方法[J]. 数学学报, 2003, 46(2): 361-368. DOI: cnki:ISSN:0583-1431.0.2003-02-020 |
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| 作者姓名： | 陈红斌 李开泰 |
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| 作者单位： | 1. 西安交通大学理学院,西安,710049;北京大学数学与应用数学实验室,北京,100871
2. 西安交通大学理学院,西安,710049 |
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| 基金项目： | 国家重大基础研究专项基金资助项目，高等学校重点实验室访问学者基金资助项目 |
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| 摘 要： | 设g∈C2(R),p(t)为连续的2π周期函数.考虑Duffing方程x+g(x)=p(t),x(O)=x(2π),x(0)=x(2π),笔者应用奇点理论,证明了Duffing算子Fx(t)=x(t)+g(x(t)).当g(x)为严格凸且g’(x)渐近跨越第一共振点0时, F整体等价于Whitney意义下的fold映射,特别地,获得2π周期解的不存在性、唯一性与唯二性定理.
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| 关 键 词： | Duffing方程 周期解 奇点理论 |
| 文章编号： | 0583-1431(2003)02-0361-08 |
| 修稿时间： | 2001-02-13 |
On Singularity Methods of the Duffing Equation |
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| Hong Bin CHENG. On Singularity Methods of the Duffing Equation[J]. Acta Mathematica Sinica, 2003, 46(2): 361-368. DOI: cnki:ISSN:0583-1431.0.2003-02-020 |
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| Authors: | Hong Bin CHENG |
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| Affiliation: | Hong Bin CHENG(Lab of Mathematics and Its Application of Peking University, Beijing 100871, P. R. China)(Department of Mathematics of Xian Jiaotong University, Xi'an 710049, P. R. China)(Fax: (029)52663320; E-mail: zhanglin@pub@xaonline.com)Kai Tai LI (Department of Mathematics of Xian Jiaotong University, Xi'an 710049, P. R. China) |
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| Abstract: | Consider the Duffing equation x + g(x) = p(t), x(0) =x(2π), x(0) = x(2π), where g ∈ C2(R) is a strictly convex function, g'(x) crosses the first resonant point asymptotically. We apply the singularity theory to obtain that Duffing operator Fx(t) = x(t) + g(x(t)) is global equivalent to the fold mapping in the sense of H. Whitney. In particular, we obtain the exact number of periodic solutions. |
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| Keywords: | Duffing equation Periodic solution Singularity theory |
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