| 关于单参数曲线族的包络与C-判别式的探讨 |
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| 引用本文： | 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].山东大学学报(理学版),2010,45(2):70-74. |
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| 作者姓名： | 李起峰 张家祯 史玉明 |
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| 作者单位： | 山东大学数学学院,山东,济南,250100 |
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| 基金项目： | 教育部科学技术研究项目 |
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| 摘 要： | 根据微分几何基本理论,单参数曲线族k(C)的包络必满足C-判别式。常微分方程中也利用此结论研究方程的奇解,然而,上述结论存在反例。本文先在一个较一般情况下得到包络满足一个较弱条件的结论。然后,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。最后,给出包络满足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。
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| 关 键 词： | 包络 C-判别式 常微分方程 隐函数存在定理 |
| 收稿时间： | 2009-02-22 |
Study on envelope of a family of curves with one parameter and its C-discriminant |
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| 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].Journal of Shandong University,2010,45(2):70-74. |
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| Authors: | LI Qi-feng ZHANG Jia-zhen SHI Yu-ming |
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| Institution: | Department of Mathematics, Shandong University, Jinan 250100, Shandong, China |
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| 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. |
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| Keywords: | envelope C-discriminant ordinary differential equation the implicit function theorem |
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