一类非线性方程的解的存在性及其应用

The Existence of the Solutions of Some Nonlinear Operator Equations and Applications

设 A是 Amann意义下的凹 (凸 )算子 .本文提出序 Lipschitz条件 ,无需考虑任何紧性或连续性条件 ,由 Mann迭代技巧证明了方程 Ax =x的解的存在性 .将所得结果应用于无界域上的 Hammerstein积分方程 。

In this paper, several existence theorems on the solutions of concave (or convex ) operator equations are obtained. The results are applied to Hammerstein integr al equations on R N, moreover, some new conclusions are given.