高阶非线性微分方程的周期解

J4 ›› 2009, Vol. 44 ›› Issue (10): 43-47.

高阶非线性微分方程的周期解

陈新一

西北民族大学中国民族信息技术研究院, 甘肃兰州 730030

收稿日期:2009-03-08 出版日期:2009-10-16 发布日期:2009-12-07
作者简介:陈新一(1957)，男，教授，主要从事微分方程的理论研究. Email: cxyxbmd@sina.com

Periodic solution of the higher order nonlinear differential equation

CHEN Xin-Yi

China Minorities Information Technology Institute, Northwest University for Nationalities, Lanzhou 730030, Gansu, China

Received:2009-03-08 Online:2009-10-16 Published:2009-12-07

摘要/Abstract

摘要：

利用重合度理论研究一类高阶时滞微分方程x⁽ⁿ⁾(t)+h(x´(t))+f(x(t))x´(t)+g(x(t-τ(t)))=p(t)周期解问题,得到T(T>0)周期解存在性的新结果,推广了已有的结果。

关键词: 高阶微分方程;周期解;重合度

Abstract:

By employing the coincidence degree, a kind of higher order differential equations with delay and the equation x⁽ⁿ⁾(t)+h(x´(t))+f(x(t))x´(t)+g(x(t-τ(t)))=p(t) are studied. Some new results on the existence of T(T>0) periodic solutions are obtained, which generalizes the known results.

Key words: higher order differential equation; periodic solution; coincidence degree

中图分类号:

Q175.6

陈新一. 高阶非线性微分方程的周期解[J]. J4, 2009, 44(10): 43-47.

CHEN Xin-Yi. Periodic solution of the higher order nonlinear differential equation[J]. J4, 2009, 44(10): 43-47.

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