关于微分方程局部解存在定理证明的注记

A note on the existence theorem of local solution for differential equation

通过对有关微分方程局部解存在定理经典证明的研究,给出了一个强化条件下的局部解存在定理,同时给出了一个一阶常微分方程解存在的简化证明和解的一般表达式,并提出教学建议。

Based on the classic proof of the existence theorem of local solution for differential equation, an existence theorem under a reinforcement condition is presented. And then we provide both simplified proof of the solution existence for first order differential equations and a general expression for the solution. Finally, some teaching suggestinns are proposed.