不动点指数及其对传染病传播模型的非线性积分方程的应用*
Fixed Point Indexes and Its Applications to Nonlinear Integral Equations Modeling Infectious Diseases
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摘要: 本文研究了一类具边界控制条件的正算子的不动点指数问题,得到了几个有较好应用价值的不动点指数为1或0的条件,以及一个更为广泛的锥拉伸与锥压缩不动点定理,推广和改进了[3,8,9]中的相应结果。作为应用,文中也讨论了传染病传播模型的非线性积分方程具正连续周期解的条件。Abstract: 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 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.
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