一类抽象二元非线性算子的不动点的存在性与唯一性

Existence and Uniqueness of Fixed Points for a Class of Abstract Binary Nonlinear Operators

该文利用半序Banach空间中的锥性质和单调迭代方法,以及相关正有界线性算子的谱半径条件,研究了一类抽象二元非线性算子的不动点的存在性和唯一性;从而推广和改进了一个经典定理,而且获得了一些新结果.最后给出了对一阶非线性常微分方程初值问题的应用.

In this paper,we study the existence and uniqueness of fixed points for a class of abstract binary nonlinear operators,by means of the properties of cone,monotone iterative methods and spectral radius conditions of related positive bounded linear operators in partially ordered Banach spaces;and then generalize and improve a classical theorem,and so obtain several new results.Finally,we present an application to initial value problems of first order nonlinear ordinary differential equations.