Fixed point indexes and its applications to nonlinear integral equations modelling infectious diseases. (English) Zbl 0731.45007
Summary: 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 a cone is obtained, which generalizes and improves the corresponding results from the literature. As an application, we utilize the results presented above to study the existence conditions of positive solutions of nonlinear integral equations modelling infectious diseases.
MSC:
| 45G10 | Other nonlinear integral equations |
| 45M20 | Positive solutions of integral equations |
| 92C60 | Medical epidemiology |
Keywords:
fixed point index; positive operators; boundary control; expansions; compressions; positive solutions; nonlinear integral equations; infectious diseasesReferences:
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