摘要
用与证明传统隐函数定理类似的方法,给出了带有有区别参数的光滑映射芽在I-P-K-等价关系下的隐函数定理及余维估计定理,得到了对带有有区别参数的光滑映射芽的奇异型进行分类的方法,从而为研究Clairaut型常微分方程与偏微分方程的分支问题提供了理论依据.
With the similar method to the one used to prove traditonal implicit function theorem, implicit function theorem and codimension estimation theorem of smooth map germs with distinguished parameters relative to I-P-H-equivalence were obtained. The classification method of singularity type of smooth map germ with distinguished parameters was discussed, which provides theoretical foundation for the studies of the bifurcations of ordinary differential equations and partial differential equations of Clairaut type.
出处
《吉林大学学报（理学版）》
CAS
CSCD
北大核心
2010年第6期936-940,共5页
Journal of Jilin University:Science Edition
基金
国家自然科学基金(批准号:10271023)
吉林省教育厅"十一五"科学技术研究项目基金(批准号:2009199)
关键词
I-P-K-等价
隐函数定理
余维
奇异型
I-P-H-equivalence
implicit function theorem
codimension
singularity type
