一类非线性二元算子方程解的存在唯一性及其应用

On the Existence and Uniqueness of Solutions for a class of Nonlinear Operator Equations and Applications

本文引入序Lipschitz条件 ,无需考虑算子的紧性 ,连续性或凹凸性 ,利用锥理论和单调迭代技巧 ,得到了方程A(x ,x) =x解的存在唯一性 .将所获得的结果应用于无界域上Hammerstein非线性积分方程 ,得到了新的结论 .

In this paper,the nonlinear operator equation A(x,x)=x is discussed.Using the cone theory and mixed monotone operator theory,an existence and uniqueness theorem of solutions of the above equation is obtained.The results one applied to Hammerstein integral equations on RN,moreover,some new conclusions are given.