抽象微分—积分方程解的混合单调迭代求法

MIXED MONOTONE ITERATION FOR SOLUTION OF ABSTRACT INTEGRO-DIFFERENTIAL EQUATION

首次应用混合单调方法,研究了Banach空间中二阶微分-积分方程边值问题u^n(t)=-f(t,u(t),Tu(t)),t∈I=[a,b]u(a)=u(b)=0解的存在与唯一性,获得了新的结果.

In this paper,for the first time,by the method of the mixed monotone,the auther study the exis-tence and uniqueness of solution for the boundary value problem of second order integro-differental equation in Banach space followingu'(t) = -f(t,u(t),Tu(t)),t∈I=[a,b],u(a) = u(b) = 0, and obtain the new result.