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Banach空间中二阶积分-微分方程的初值问题
引用本文:王文霞.Banach空间中二阶积分-微分方程的初值问题[J].应用泛函分析学报,2003,5(2):132-142.
作者姓名:王文霞
作者单位:郑州大学数学系,河南,郑州,460052;太原师范学院数学系,山西,太原,030012
基金项目:SupportedbyNaturalScienceFoundationofShanxi(991003)
摘    要:使用锥理论及单调迭代技术,首先讨论了Banach空间中一阶积分-微分方程初值问题的最小最大解的存在性,并在此基础上讨论了带有一阶微分项的二阶积分-微分方程初值问题的最小最大解的存在性。

关 键 词:Banach空间  积分-微分方程  初值问题  锥理论  单调迭代  最大解  最小解  存在性

Initial Value Problems for Second-order Integro-differential Equations in Banach Space
WANG Wen-xia.Initial Value Problems for Second-order Integro-differential Equations in Banach Space[J].Acta Analysis Functionalis Applicata,2003,5(2):132-142.
Authors:WANG Wen-xia
Abstract:In this paper, by using the cone theory and the monotone iterative technique, the existence of maximal and minimal solutions of initial value problems for one-order integro-differential equations in Banach space is firstly investigated, and the existence of maximal and minimal solutions of initial value problems for second order integro-differential equations which depends on x′ in Banach space is discussed by the results of one-order integro-differential equation.
Keywords:integro-differential equation  initial value problem  ordered Banach space  maximal and minimal solutions
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