抽象空间中微分方程初值问题解的探析  

Analysis of the Solution of Initial Value Problem for Differential Equations in Abstract Spaces

作　　者：刘洪运[1] 张瑞玲[2] 

机构地区：[1]河南师范大学,河南新乡453000 [2]商丘职业技术学院,河南商丘476000

出　　处：《河南科学》2008年第3期253-255,共3页Henan Science

基　　金：国家自然科学基金计划资助项目(60572001)

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.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.

关 键 词：Cauchy-Peano定理 抽象空间 微分方程 初值问题解的存在性 

分 类 号：O175.15[理学—数学]