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

李晓静;鲁世平

系统科学与数学 ›› 2009, Vol. 29 ›› Issue (8) : 1079-1087.

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系统科学与数学 ›› 2009, Vol. 29 ›› Issue (8) : 1079-1087. DOI: 10.12341/jssms08380
论文

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

    李晓静(1),鲁世平(2)
作者信息 +

The Existence of Periodic Solutions for a Kind of High-Order Duffing Equations with Sign-Changing Coefficient Ahead of Nonlinear Term

    LI Xiaojing(1), LU Shiping(2)
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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)+β(t)g(x(t−τ(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β(t)可变号,但是,周期解先验界估计方法与已有工作不同.

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.

关键词

高阶 / Duffing方程 / 重合度 / 周期解.

Key words

High-order / duffing equation / coincidence degree / periodic solution.

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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. 系统科学与数学, 2009, 29(8): 1079-1087. https://doi.org/10.12341/jssms08380
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. Journal of Systems Science and Mathematical Sciences, 2009, 29(8): 1079-1087 https://doi.org/10.12341/jssms08380
中图分类号： 34C25   
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