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<sup>*</sup>

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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^*

基金项目: * 国家自然科学基金资助项目

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.

[1]	Fitzpatrick,P.M.and W.P.Petryshyn,Fixed point theorems and the fixed point index for multivalued maps in cones.J.London.Math.Soc.,12,2(1975).75-85.
[2]	Guo.D.,Some fixed point theorems and applications,Nonl.Anal.,10(1986),1293-1302.
[3]	郭大钧,《非线性泛函分析》,山东科学技术出版社(1985).
[4]	Potter,A.J.B,Applications of Hilbert's prejective metrie to certain classes of nonhomogeneous operator(?),Quarl J Math.,Oxford.28(1977) 93-96.
[5]	Nussbaum.R.,A penodicity threshold theoiem forme nonlinear integral equations,SIAM J.Math.Anal..9(1978).356-376.
[6]	Williams,L.R.and R.W.Legget.Nonzeros of nonlinear integral equations modelieg infectious disease,SIAM J.Math.Anal..13(?)112-121.
[7]	郭大钧,传染病模型的非线性积分方程的解的个数,数学年刊,8,1(1987),27-31.
[8]	Legget,R.W.and L.R.Williams,A fixed point theorem with applications to an infectious disease model.J.Math.Anal.Appl.,76(1980),91-97.
[9]	杜旭光,非线性算子的不动点及固有值,科学通报,5(1983),201-265.