一类非线性算子方程解的存在性及应用

EXISTENCE OF SOLUTIONS FOR A CLASS OF NONLINEAR OPERATOR EQUATIONS AND APPLICATIONS

在不假定锥正规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解的存在性定理，并应用到Ｂａｎａｃｈ空间中常微分方程的初值问题．

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 normality of cone. The results obstained are applied to the initial value problem for ordinary differential equations in Banach spaces.