| 一类非线性项前系数可变号的高阶Duffing方程的周期解存在性问题 |
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| 引用本文： | 李晓静,鲁世平.一类非线性项前系数可变号的高阶Duffing方程的周期解存在性问题[J].系统科学与数学,2009,29(8):1079-1087. |
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| 作者姓名： | 李晓静 鲁世平 |
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| 作者单位： | 1. 江苏技术师范学院数理学院,常州,213001;安徽师范大学数学系,芜湖,241000
2. 安徽师范大学数学系,芜湖,241000 |
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| 基金项目： | 安徽省自然科学基金，安徽省教育厅自然科学基金重点项目，江苏技术师范学院青年科研基金项目(KYY08033)资助课题 |
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| 摘 要： | 利用Fourier级数理论,伯努利数理论和重合度理论研究了一类具偏差变元的高阶泛函微分方程$x^{(m)}(t)+\beta (t)g(x(t-\tau(t)))=p(t)$的周期解问题,得到了周期解存在性的新结论,有意义的是非线性项前的系数$\beta(t)$可变号,但是,周期解先验界估计方法与已有工作不同.
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| 关 键 词： | 高阶 Duffing方程 重合度 周期解. |
| 收稿时间： | 2008-1-7 |
| 修稿时间： | 2008-5-9 |
THE EXISTENCE OF PERIODIC SOLUTIONS FOR A KIND OF HIGH-ORDER DUFFING EQUATIONS WITH SIGN-CHANGING COEFFICIENT AHEAD OF NONLINEAR TERM |
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| LI Xiaojing,LU Shiping.THE EXISTENCE OF PERIODIC SOLUTIONS FOR A KIND OF HIGH-ORDER DUFFING EQUATIONS WITH SIGN-CHANGING COEFFICIENT AHEAD OF NONLINEAR TERM[J].Journal of Systems Science and Mathematical Sciences,2009,29(8):1079-1087. |
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| Authors: | LI Xiaojing LU Shiping |
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| Institution: | (1)College of Mathematics and Physics, Jiangsu Teachers University of Technology, Changzhou 213001;Department of Mathematics, Anhui Normal University, Wuhu 241000;(2)Department of Mathematics, Anhui Normal University, Wuhu 241000. |
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| Abstract: | In this paper, by using the theory of Fourier series, Bernoulli number theory and continuation theorem of coincidence degree theory, we study a kind of high-order functional differential equation with a deviating argument as follows:x^{(m)}(t)+\beta (t)g(x(t-\tau(t)))=p(t). Some new results on the existence of periodic solutions are obtained. Here the sign of \beta(t) can be changed. But, the methods to estimate a priori bounds of periodic solutions are different from the corresponding ones of the past. |
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| Keywords: | High-order duffing equation coincidence degree periodic solution |
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