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:
作者单位
冯兆生 北方交通大学数学系 
费树岷 东南大学自动化所 
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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.
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