一类超线性算子的正不动点的存在唯一性及应用

The Existence and Uniqueness and Applications of Positive Fixed Points for a Class of Superlinear Operators

研究了一类超线性齐次算子的正不动点的存在唯一性问题.利用全序集的性质讨论了超线性齐次算子的性质,基于这些性质,通过分析方法得到了抽象空间中超线性齐次算子的一个新的正不动点的存在唯一性定理.利用本文所获得的结果,研究了一类超线性Hammerstein型积分方程正解的存在唯一问题,获得了此类积分方程存在唯一正解的充分条件,并给出了解的表示.

Existence and uniqueness of fixed points for a class of superlinear homogeneous operators was inves- tigated. Some properties of the homogeneous operator were given by using the property of complete order set. Based on these properties, a new result on existence and uniqueness of positive fixed point for homogeneous operator was obtained by using analytical methods. By virtue of the fixed point result, the unique positive solution of a kind of Hammerstein type integral equations was investigated and the expression of the solution was given.