非线性分析中的半序方法

Method of partial ordering in nonlinear analysis

系统论述了利用半序方法研究缺乏紧性和缺乏连续性的增算子、减算子以及混合单调算子最大不动点和最小不动点的存在性、不动点的存在唯一性、迭代序列的收敛性以及收敛速率估计等问题。

This paper gives a survey on the existence of maximal and minimal fixed points and existence and uniqueness of fixed points for non compact and discontinuous increasing operators, decreasing operators and mixed monotone operators by means of method of partial ordering. Convergence of iterative sequences and estimation of the convergence rate are also discussed and applications to nonlinear integro differential equations in Banach spaces are given. In addition, some problems for further investigation are offered.