Banach空间一类非线性算子方程的迭代求解及应用

Iterative Technique for a Class of Nonlinear Operator Equations in Banach Spaces and Applications

在不假定锥正规、再生和算子连续的条件下,利用锥理论和单调迭代方法证明了一类非线性算子方程x=A(x,x)解的存在性定理,并应用于Banach空间一阶微分方程的终值问题.

In this paper, we use the cone theory and monotone iterative technique to prove the existence theorems of solutions for a class of nonlinear operator equations without the assumption of continuity and generating normality of cone. The results obtained are applied to terminal value problems for differential equations on unbounded domains in Banach spaces.