关于单参数曲线族的包络与C-判别式的探讨

J4 ›› 2010, Vol. 45 ›› Issue (2): 70-74.

关于单参数曲线族的包络与C-判别式的探讨

李起峰，张家祯，史玉明

山东大学数学学院, 山东济南 250100

收稿日期:2009-02-22 出版日期:2010-02-16 发布日期:2010-03-27
通讯作者: 史玉明(1963-), 女, 博士, 博士生导师, 研究方向为微分方程与动力系统.Email: ymshi@sdu.edu.cn
作者简介:李起峰(1988-), 男, 主要研究方向为代数几何. Email: limonkey18@163.com
基金资助:
山东省自然科学基金资助项目 (Y2006A15)

Study on envelope of a family of curves with one parameterand its C-discriminant

Department of Mathematics, Shandong University, Jinan 250100, Shandong, China

Received:2009-02-22 Online:2010-02-16 Published:2010-03-27

摘要/Abstract

摘要：

在一个较一般情况下得到包络满足一个较弱条件的结论，利用此结论, 得到在一些较易验证且不失一般性的条件之下包络满足的条件。给出了包络满足C-判别式的条件, 并给出了求常微分方程奇解的一个实用方法。

关键词: 包络; C-判别式; 常微分方程; 隐函数存在定理

Abstract:

A weak condition satisfied by the envelope is given under certain general assumptions. Based on it, some conditions on the family of curves, which can be easily tested, are given. Finally, the conditions that satisfied C-discriminant are given so that its envelope, and an applicable method of obtaining singular solutions of ordinary differential equations is proposed.

Key words: envelope; C-discriminant; ordinary differential equation; the implicit function theorem

李起峰张家祯史玉明. 关于单参数曲线族的包络与C-判别式的探讨[J]. J4, 2010, 45(2): 70-74.

LI Qi-Feng, ZHANG Jia-Zhen, SHI Yu-Ming. Study on envelope of a family of curves with one parameterand its C-discriminant[J]. J4, 2010, 45(2): 70-74.

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