Banach空间中二元非线性算子方程的迭代求解

Interative Technique for a Class of Nonlinear Operator Equations in Banach Spaces

在Ｂａｎａｃｈ空间中，利用锥理论和混合单调算子性质，研究了更为一般的非线性算子方程ｕ＝Ａ（ｕ，ｕ）解的存在与唯一性，给出了逼近解的迭代序列和误差估计。

Abstract In this paper, the nonlinear operator equation u=A(u,u) in a Banach space is considered. Using the cone theory and mixed monotone operator theory, some existence and uniquence theorems of solutions of the above equation are obtained.