| Liénard方程周期解的存在唯一与唯二性问题 |
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| 引用本文： | 陈红斌,李开泰,李东升.Liénard方程周期解的存在唯一与唯二性问题[J].数学学报,2004,47(3):417-424. |
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| 作者姓名： | 陈红斌 李开泰 李东升 |
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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经费(G1999032801-07)，自然科学基金(50136030)，高校重点实验室访问学者基金 |
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| 摘 要： | 本文考虑微分方程 x+f(x)x+g(x)=p(t),其中g∈C~1(R)为严格递减,f ∈ C(R),p(t)为2π周期的连续函数,给出周期解的存在唯一的充要条件;在f(x)=c,g(x)严格凸函数且跨越第一共振点零时,给出唯二性定理。
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| 关 键 词： | Lienard方程 周期解 延拓定理 |
| 文章编号： | 0583-1431(2004)03-0417-08 |
| 修稿时间： | 2002年11月27 |
On the Existence of Exactly One and Two Periodic Solutions of Liénard Equation |
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| Hong Bin CHEN School of Science of Xi'an Jiaotong University,Xi'an ,P. R. China Lab of Mathematics and Its Application of Peking University,Beijing ,P. R. China Kai Tai LI Dong Sheng LI School of Science of Xi'an Jiaotong University,Xi'an ,P. R. China.On the Existence of Exactly One and Two Periodic Solutions of Liénard Equation[J].Acta Mathematica Sinica,2004,47(3):417-424. |
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| Authors: | Hong Bin CHEN School of Science of Xi'an Jiaotong University Xi'an P R China Lab of Mathematics and Its Application of Peking University Beijing P R China Kai Tai LI Dong Sheng LI School of Science of Xi'an Jiaotong University Xi'an P R China |
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| Institution: | Hong Bin CHEN School of Science of Xi'an Jiaotong University, Xi'an 710049, P. R. China Lab of Mathematics and Its Application of Peking University, Beijing 100871, P. R. China Kai Tai LI Dong Sheng LI School of Science of Xi'an Jiaotong University, Xi'an 710049, P. R. China |
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| Abstract: | In this paper, we consider the Lienard equation +f(x) +g(x) =p(t),
where g∈C~1(R), f∈C(R), p(t)∈C_(2π). A necessary and sufficient condition to ensure
the existence and uniqueness of a 2π-periodic solution is obtained, for the Duffing type
equation. For the Ambrossetti-Prodi type, +c+ g(x,t) =s, the existence of exactly
two periodic solutions is confirmed by Sturm theory. |
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| Keywords: | Lienard equation Periodic solution Continuation theorem |
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