A new proof of the implicit function theorem

Journal of Shanghai Normal University (Natural Sciences)

HAN Maoan¹  SHENG Lijuan¹ 

[1] College of Mathematics and Science, Shanghai Normal University;

关键词: implicit function theorem;    differential equation;    existence and uniqueness of solutions;    dependence on initial conditions and parameters;   

DOI  :  10.3969/J.ISSN.100-5137.2016.03.010

来源: DOAJ

【 摘 要 】

The implicit function theorem plays an important role in the mathematical analysis and many other branches of mathematics. In the college course of Ordinary Differential Equations, we have learnt the theorems on the existence and uniqueness of solutions and dependence on initial values and parameters. In this paper, by using these theorems of differential equations, we give a new proof for the implicit function theorem.

【 授权许可】

Unknown