Banach空间中二阶积分-微分方程的初值问题(英文)

Initial Value Problems for Second-order Integro-differential Equations in Banach Space

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.

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.