奇异减算子的不动点定理及其应用

The Fixed Point Theorems for a Class of Singular Nonincreasing Operators and its Applications

提出了一类新的概念——奇异减算子,并对该类算子的不动点的存在性进行了讨论,得到了奇异减算子的不动点的存在唯一性的几个定理。这些定理推广了已有的结果。同时将这些定理应用到奇异边值问题,得到奇异边值问题正解的存在唯一性。

A new class of operators——singular nonincreasing operators is given. The existence of fixed point for these op-erators and obtains some fixed point theorems on the existence and uniqueness is discussed. The theorems obtained improve theknown conclusions. In the meantime, the theorems applied to the singular boundary value problems.