一类非线性方程的解的存在唯一性及其应用

The Exitence and Uniqueness of the Solutions of Some Nonlinear Operator Equations and Applications

设 A是增算子或减算子 .本文引入广义序 Lipschitz条件 ,不要求算子的任何紧性、连续性或凹凸性 ,由单调迭代技巧得到了方程 Ax=x的解的存在唯一性 .将所得结果应用于无界域上的 Hammerstein积分方程 ,得到了新结果 .

In this paper, the existence and uniqueness of the solutions of increasing or decreasing operator equations are investigated. The results are applied to Hammerstein integral equations on R N, moreover, some new conclusions are given.