| 引用本文： |
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秦发金,姚晓洁.一类具脉冲时滞Rayleigh型方程的周期解[J].广西科学,2007,14(4):348-351,353. [点击复制]
- QIN Fa-jin,YAO Xiao-jie.Periodic Solutions of the Rayleigh Equation with Delays and Impulses[J].Guangxi Sciences,2007,14(4):348-351,353. [点击复制]
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| 摘要: |
| 利用重合度理论,研究一类具脉冲时滞的Rayleigh型方程x″(t)+f(t,x'(t-δ))+g(t,x(t-τ(t)))=p(t),t≠ti,Δx(ti)=Ii(x(ti),x'(ti)),Δx'(ti)=Ji(x(ti),x'(ti))周期解的存在性问题.在不要求∫0Tp(t)dt=0的条件下,得到其周期解存在的2组充分条件,推广和改进了已经报道的相关结果. |
| 关键词: Rayleigh型方程 脉冲 周期解 存在性 重合度 |
| DOI： |
| 投稿时间：2006-12-22修订日期：2007-01-12 |
| 基金项目: |
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| Periodic Solutions of the Rayleigh Equation with Delays and Impulses |
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QIN Fa-jin1,2, YAO Xiao-jie1
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| (1.Department of Mathematics and Computer Science, Liuzhou Teachers College, Liuzhou, Guangxi, 545004, China;2.Mathematical College, Sichuan University, Chendu, Sichuan, 610064, China) |
| Abstract: |
| By means of the coincidence degree theory, we study the existence of periodic solutions of the Rayliegh equation x″ (t)+f (t, x' (t-δ))+g (t, x (t-τ (t)))=p (t), t≠ti, x (ti)=Ii (x (ti), x' (ti)), x' (ti)=Ji (x (ti), x' (ti))with delays and impulses.Some new sufficient conditions of periodic solutions are obtained without requiring∫T0p (t)dt=0.The results have extend and improved the related reports in the literatures. |
| Key words: Rayleigh equation impulses periodic solutions existence coincidence degree |
