[1]佘志炜,王全义.一类二阶微分方程周期解的存在性[J].华侨大学学报(自然科学版),2010,31(2):235-240.[doi:10.11830/ISSN.1000-5013.2010.02.0235]
　SHE Zhi-wei,WANG Quan-yi.Existence of Periodic Solutions for a Class of Second Order Differential Equations[J].Journal of Huaqiao University(Natural Science),2010,31(2):235-240.[doi:10.11830/ISSN.1000-5013.2010.02.0235]
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一类二阶微分方程周期解的存在性()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第31卷
期数:
2010年第2期
页码:
235-240
栏目:
出版日期:
2010-03-20

文章信息/Info

Title:
Existence of Periodic Solutions for a Class of Second Order Differential Equations
文章编号:
1000-5013(2010)02-0235-06
作者:
佘志炜; 王全义
华侨大学数学科学学院
Author(s):
SHE Zhi-wei;  WANG Quan-yi
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
微分方程;  周期解;  重合度;  偏差变元;  存在性
Keywords:
differential equation;  periodic solution;  coincidence degree;  deviating argument;  existence
分类号:
O175.14
DOI:
10.11830/ISSN.1000-5013.2010.02.0235
文献标志码:
A
摘要:
研究一类具有偏差变元的二阶微分方程x″(t)+f(x′(t))+h(x(t))x′(t)+g(t,x(t-τ(t)))=p(t)的周期解的存在性问题.通过应用Schwarz不等式,Minkowski不等式,以及重合度理论,在满足一定条件下,得到方程至少存在一个T-周期解的新结果,且其周期解存在性的充分条件并不要求h(x)是有界函数.
Abstract:
In this paper,we study the problem on the existence of periodic solutions for a class of second order differential equations with a deviating argument x″(t)+f(x′(t))+h(x(t))x′(t)+g(t,x(t-τ(t)))=p(t).By means of Schwarz’s inequality and Minkowski’s inequality and the coincidence degree theory,a new result on the existence of periodic solutions for the equations is obtained under some conditions.In the sufficient conditions of the existence of periodic solutions for the equations,the bounded function h(x) may not be required.

参考文献/References:

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备注/Memo

备注/Memo:
福建省自然科学基金资助项目(Z0511026)
更新日期/Last Update: 2014-03-23