Applied Mathematics and Mechanics (English Edition) ›› 1989, Vol. 10 ›› Issue (5): 399-406.

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

Zhang Shi-sheng1, Bian Wen-ming2   

  1. 1. Sichuan University, Chengdu;
    2. Henan Normal University, Kaifeng
  • Received:1988-01-13 Online:1989-05-18 Published:1989-05-18
  • Supported by:
    Project supported by National Natural Science Foundation of China

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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