非线性算子方程迭代解的存在性定理及其应用

在Ｂａｎａｃｈ空间中，利用锥理论和单调迭代方法研究了一类非线性算子方程的解和最小最大耦合解的存在与迭代逼近定理，并应用到Ｂａｎａｃｈ空间中非线性Ｖｏｌｔｅｒｒａ型积分方程和常微分方程的初值问题．

Existence Theorems of Iterative Solutions for Nonlinear Operator Equations and Applications

In this paper, the author uses the cone theory and monotone iterative technique to study an existence and iterative approximation theorem of solutions and coupled minimal and maximal quasi solutions for a class of nonlinear operator equations in ordered Banach spaces, and gives two applications to nonlinear Volterra type integral equations and the initial value problems for ordinary differential equations in Banach spaces.