具偏差变元的高阶泛函微分方程的周期解存在性问题

李晓静;鲁世平

系统科学与数学 ›› 2009, Vol. 29 ›› Issue (3) : 367-377.

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中国科学院数学与系统科学研究院期刊网
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系统科学与数学 ›› 2009, Vol. 29 ›› Issue (3) : 367-377. DOI: 10.12341/jssms10181
论文

具偏差变元的高阶泛函微分方程的周期解存在性问题

    李晓静(1), 鲁世平(2)
作者信息 +

The Existence of Periodic Solutions for a Kind of High-Order Functional Differential Equation

    LI Xiaojing(1), LU Shiping(2)
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文章历史 +

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)+\sum^{m-1}\limits_{i=1}a_{i}x^{(i)}(t)+f(x(t))+\beta (t)g(x(t-\tau(t)))=p(t)的周期解问题,得到了周期解存在的充分条件,有意义的是函数\beta(t)可变号.

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 equations with a deviating argument is considered. Some new results on the existence of periodic solutions are obtained.

关键词

高阶泛函微分方程 / 重合度 / 周期解.

Key words

High-order functional differential equation / coincidence degree / periodic solution.

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李晓静 , 鲁世平. 具偏差变元的高阶泛函微分方程的周期解存在性问题. 系统科学与数学, 2009, 29(3): 367-377. https://doi.org/10.12341/jssms10181
LI Xiaojing , LU Shiping. The Existence of Periodic Solutions for a Kind of High-Order Functional Differential Equation. Journal of Systems Science and Mathematical Sciences, 2009, 29(3): 367-377 https://doi.org/10.12341/jssms10181
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