本文在一般Banach空间中讨论微分方程的初值问题：u＇＝f（t，u），u（0）＝x0．设f（t，u）不连续，仅满足所谓弱Caratheodory条件，但仍证明了初值问题的解可由迭代序列的一致极限得到，并给出了逼近解的迭代序列的误差估计．对周期过值问题得到了类似的结果．

In this paper, it presents the initial value problem of the ordinary differential equations U' = f(t, u) in general Banach spaces. We assume that f(t, u) is not continuous and only f(t, u) satisfies the weak Caratheodory condition, we proved, however,that the solution of the initial value problem can be obtained by the uniformly limit of the iterative sequences. The error estimate of the iterative sequences of approximation solution is given. And also we have obtained the similar result to the periodic boundary value problem.