摘要
本文在一般序Ｂａｎａｃｈ空间中研究了不连续非线性Ｖｏｌｔｅｒｒａ型积分方程的唯一解．在非常弱的条件下证明了非线性Ｖｏｌｔｅｒｒａ型积分方程的唯一解可以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式，然后应用到一阶微分方程的初值问题，本质改进并推广了最近的一些结果．
In this paper, the unique solution of the discontinuous nonlinear Volterra type integral equations in Banach spaces are investigated. In very weakly condition the unique solution of nonlinear Volterra type integral equations can be obtained by the uniformly limit of the iterative sequences is proved. The error estimate of the iterative sequences of approximation solutions is given. And then apply this result to the initial value problem of first order ordinary differential equations. The results obtained here improve and extend recent results.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2001年第1期131-136,共6页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目(19871048)
山东省自然科学基金资助
