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| 抽象空间中微分方程初值问题解的探析 | |
| 引用本文： | 刘洪运,张瑞玲. 抽象空间中微分方程初值问题解的探析[J]. 河南科学, 2008, 26(3): 253-255 |
| 作者姓名： | 刘洪运 张瑞玲 |
| 作者单位： | 河南师范大学,河南,新乡,453000;商丘职业技术学院,河南,商丘,476000;商丘职业技术学院,河南,商丘,476000 |
| 摘 要： | 通过反例,证明了著名的Cauchy-Peano定理在抽象空间中具有一定的局限性.对该定理加以改进和推广,并构造有关连续映象,利用Krasnoselskii不动点定理证明了改进后结果的正确性. |
| 关 键 词： | cauchy-Peano定理 抽象空间 微分方程 初值问题解的存在性 |
| 文章编号： | 1004-3918(2008)03-0253-03 |
| 修稿时间： | 2007-11-28 |
Analysis of the Solution of Initial Value Problem for Differential Equations in Abstract Spaces |
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| Liu Hongyun,Zhang Ruiling. Analysis of the Solution of Initial Value Problem for Differential Equations in Abstract Spaces[J]. Henan Science, 2008, 26(3): 253-255 | |
| Authors: | Liu Hongyun Zhang Ruiling |
| Affiliation: | Liu Hongyun1,2,Zhang Ruiling2(1.Henan Normal University,Xinxiang 453000,China,2.Shangqiu Vocational , Technical College,Shangqiu 476000,China) |
| Abstract: | By use of anti-cases,it has been proved that the limitations of well-known Cauchy-Peano theorem in abstract spaces.The improvement and generalization for the theorem,and construction of relevant continuous mapping,as well as the employment of Krasnoselskii fixed point theorem proved correctness of the result being improved. |
| Keywords: | Cauchy-Peano theorem abstract spaces differential equations the existence of initial value problem |
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