| Lienard方程周期解、概周期解的存在性 |
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| 引用本文： | 林发兴.Lienard方程周期解、概周期解的存在性[J].数学学报,1996,39(3):314-318. |
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| 作者姓名： | 林发兴 |
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| 作者单位： | 福州大学数学系 |
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| 摘 要： | 本文考虑Ｌｉｅｎａｒｄ方程ｘ”十ｆ（ｘ）ｘ’＋ｇ（ｘ）＝ｅ（ｔ），我们得到：当且时，对于任意周期或概周期。数ｅ（ｔ），它有周期或概周期解．而对于Ｌｉｅｎａｒｄ方程ｘ”＋ｆ（ｘ）ｘ’＋ｃｘ＝ｅ（ｔ），我们得到：当ｃ＞０且时，对于任意周期、或概周期函数ｅ（ｔ），它有周期或概周期解．
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| 关 键 词： | Lienard方程，概周期，指数型二分性，解一致渐近稳定 |
| 收稿时间： | 1994-4-25 |
The Existence on Periodic Solutions and Almost Periodic Solutions of Lienard Equation |
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| Lin Faxing.The Existence on Periodic Solutions and Almost Periodic Solutions of Lienard Equation[J].Acta Mathematica Sinica,1996,39(3):314-318. |
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| Authors: | Lin Faxing |
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| Institution: | Lin Faxing(Department of Mathematics, Fuzhou University, Fuzhou 350002, China) |
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| Abstract: | We consider Lienard equation X" f(x)x' g(x) =e(t) and obtain that if and for any periodic function or almost periodic function e(t) it has a periodic solution or almost periodic solution. For Lienard equation X" f(x)x' ex = e(t), we obtain that if and for any periodic function or almost periodic function e(t) it has a periodic solution or an almost periodic solution. |
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| Keywords: | Lienard equation almost periodic exponential dichotomy uniformly asymptotically stable solutions |
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