微分方程和差分方程的多解存在性  

The Existence of Multiple Solutions to Differential Equation and Difference Equation

作　　者：吴树宏[1] 

机构地区：[1]武汉理工大学理学院数学系,武汉430070

出　　处：《工程数学学报》2009年第5期895-905,共11页Chinese Journal of Engineering Mathematics

摘　　要：本文首先讨论了差映射的一个映射性质:某元有无映射原象等价于映射象集是否包含此元,等价于以此元为象的映射方程的解是否存在。若有两个映射,其中一个映射的象集较大,另一个映射的象集较小,则在一定条件下,可以确定此二映射的差映射象集包含一集合,此集合的差映射原象非空,以此集合中的元为映射象的差映射方程的解存在。其次,我们运用此结论讨论了几个微分方程、差分方程多解的存在性。A mapping property of difference mapping is studied in this paper at first. The main idea is whether there exists original of an element under a mapping is equivalent to whether the mapping image set contains the element and is equivalent to whether there exist the solution for the mapping equation whose mapping image is the element. If there are two mappings,one s image set is larger than the other s image set. Under the proper condition we can ascertain that the image set of the difference mapping of these two mappings contains a set, original of the set under the difference mapping is not empty, there exist solutions for the difference mapping equation such that the element of the set is mapping image. Finally, we used the obtained results to discuss the existence of multiple solutions of differential equations and a difference equation.

关 键 词：微分方程 差分方程 多解 存在性 

分 类 号：O175.1[理学—数学]