广义积分微分系统边值问题的单调迭代法

MONOTONE ITERATIVE TECHNIQUE FOR BOUNDARY VALUE PROBLEMS OF SINGULAR INTEGRO-DIFFERENTIAL SYSTEMS

单调迭代法与上、下解结合是证明非线性系统解的存在性的强有力的工具。使用这种方法研究非线性问题的解，不仅可以得到闭扇形区域上解的存在性结果。而且还可以提供求数值解的方案。本文应用单调迭代法，在假设所包含的函数关于积分项是不减的条件下，得到了解的存在性的构造性证明。所构造序列是线性系统的解，所以较易计算。并且这一证明促进了单调迭代法在广义积分微分系统的发展。

The method of upper and lower solutions, coupled with the monotone iterative technique is a powerful tool for proving the existence of solutions of nonlinear systems. The iteration schemes offer theoretical as well as constructive, existence result in a closed set namely, the sector. The upper and lower solutions that generate the sector serve as upper and lower bounds for solutions. In this paper, we consider boundary value problems (BVP) for singular integro-differential systems by using monotone iterative technique when the function involved is assume to be nondecreasing relative to integral terms. The existence of solutions is obtained as limits of monotone sequences. Each member of these sequences is a solution of singular linear systems which can explicitly be computed. Our result extends to singular integrodifferential systems from normal systems. This paper promotes the development of monotoneiterative technique in singular integro-differential systems.