一类非线性算子方程的上下解准则及应用

The Supersolution and Subsolution Criterion for a Nonlinear Operator Equation and Applications

研究了有序 Banach空间中的算子方程 Lu =f (u)的可解性及单调迭代求解方法 ,其中 L为无界闭线性算子 ,f为非线性算子。建立了该方程解存在的上、下解定理 ,所得结果概括和统一了常微分方程 ,偏微分方程及抽象微分方程中的有关结果。

The paper makes a research for the solvability of the operator equation Lu=f(u) in a ordered Banach space.Here L is a unbounded closed linear operator,and f if a nonlinear operator.The supersolution and subsolution theorems for the equation are established.The conclusions generalize and unify the relevant results in ordinary differential equations,partial differential equations and abstract space differential equatins.