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Banach空间中不连续非线性Volterra型积分方程的唯一解
引用本文:刘立山.Banach空间中不连续非线性Volterra型积分方程的唯一解[J].数学学报,2001,44(1):131-136.
作者姓名:刘立山
作者单位:曲阜师范大学数学系
基金项目:国家自然科学基金资助项目(19871048);山东省自然科学基金资助项目
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.

关 键 词:序Bnanch空间  不连续  Volterra型积分方程  逼近解
文章编号:0583-1431(2001)01-0131-06
修稿时间:1999年5月24日

The Unique Solution for Discontinuous Nonlinear Volterra Type Integral Equations in Banach Spaces
LIU Li Shan.The Unique Solution for Discontinuous Nonlinear Volterra Type Integral Equations in Banach Spaces[J].Acta Mathematica Sinica,2001,44(1):131-136.
Authors:LIU Li Shan
Institution:LIU Li Shan (Department of Mathematics, Qufu Normal University, Qufu 273165, P. R. China) (E-mail: lls@qfnu.edu.cn)
Abstract: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.
Keywords:Ordered Banach space  Discontinuous  Volterra type integral equation' Approximation soluti?
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