FIXED POINT INDEXES AND ITS APPLICATIONS TO NONLINEAR INTEGRAL EQUATIONS MODELLING INFECTIOUS DISEASES

In this paper the fixed point index problem for a class of positive operators with boundary control conditions is discussed,and some sufficient conditions for the fixed pointindex to be equal to1 or 0 are given.Moreover,a general fixed point theorem of expansions and compressions for cone is obtained,which generalizes and improves the corresponding results of[3,8,9].As an application,we utilize the results presented above to study the existence conditions of positive solutions of nonlinear integral equations modelling infectious diseases.     

泛函的一种次微分及其应用

本文定义了赋范线性空间上泛函的一种新型集值导数(γ-次微分)，讨论了它的一些性质及其在非光滑数学规划问题上的一些应用.     

Variable structure control of indefinite-dimensional systems

ＶＡＲＩＡＢＬＥＳＴＲＵＣＴＵＲＥＣＯＮＴＲＯＬＯＦＩＮＤＥＦＩＮＩＴＥ－ＤＩＭＥＮＳＩＯＮＡＬＳＹＳＴＥＭＳＬｉＷｅｎ－ｌｉｎ（李文林）ＢｉａｎＷｅｎ－ｍｉｎｇ（边文明）（ＤｅｐａｒｔｍｅｎｔｏｆＭｅｔｈｅｍａｔｉｃｓ,ＨｅｎａｎＮｏｒｍａｌＵｎｉ...     

Fixed point indexes and its applications to nonlinear integral equations modelling infectious diseases

In this paper the fixed point index problem for a class of positive operators with boundary control conditions is discussed, and some sufficient conditions for the fixed point index to be equal to 1 or 0 are given. Moreover, a general fixed point theorem of expansions and compressions for cone is obtained, which generalizes and improves the corresponding results of [3,8,9]. As an application, we utilize the results presented above to study the existence conditions of positive solutions of nonlinear integral equations modelling infectious diseases.Project supported by National Natural Science Foundation of China.     

算子方程解的稠密性及半线性系统的近似可控性

本文利用Ｂａｎａｃｈ不动点定理和Ｓｃｈａｕｄｅｒ不动点定理研究如下算子方程解的稠密性：ｙ＝ｙ０＋ＬＦ（ｙ）＋ＬＨ（ｖ）（其中，Ｌ、Ｈ为线性算子，Ｆ为非线性算子），然后，利用所得结论讨论Ｂａｎａｃｈ空间内的半线性系统：ｘ＇（ｔ）＋Ａ（ｔ）ｘ（ｔ）＝ｆ（ｔ，ｘ（ｔ）＋Ｂｕ（ｔ）的近似可控性。