冯兆生,费树岷.关于一类微分方程周期解的存在性的注记(英文)[J].数学研究及应用,1998,18(3):384~390 |
关于一类微分方程周期解的存在性的注记(英文) |
Note on Existence of Periodic Solutions of One Class Differential Equations |
投稿时间:1995-12-21 |
DOI:10.3770/j.issn:1000-341X.1998.03.011 |
中文关键词: |
英文关键词:differential equation periodic solution existence transformation. |
基金项目: |
|
摘要点击次数: 2265 |
全文下载次数: 1581 |
中文摘要: |
本文主要探讨下列周期系数微分方程dy/dt=(A1(t)y+A2(t)y2+A3(t)y3)/(a0(t)+a1(t)y+a2(t)y2)(**)的周期解个数问题,利用方程(**)解的差率法得到了方程(**)周期解的个数定理.本文仅在Ai(t),aj(t)(i=1,2,3,j=0,1,2)是连续周期函数的条件下得到这一结论,从而减弱了文[2]中相应定理的条件,即Ai(t),aj(t)均是连续可微的周期函数. |
英文摘要: |
In the present paper we investigate the number of periodic solutions of the following differential equation dy/dt=(A1(t)y+A2(t)y2+A3(t)y3)/(a0(t)+a1(t)y+a2(t)y2)(**) which was discussed in paper , and obtain the theorem by the method of cross-ratio of the solutions of (**) without the traditional condition assumption that the functions Ai(t),aj(t) (i=1,2,3; j=0,1,2) are differential. |
查看全文 查看/发表评论 下载PDF阅读器 |