### Positive periodic solutions of superlinear systems of integral equations depending on parameters

#### Abstract

A class of superlinear system of integral equations depending on multi

parameters is considered. It is shown that there are three mutually

exclusive and exhaustive subsets $\Theta _{1},\Gamma $ and $\Theta _{2}$ of

the parameter space such that there exist at least two positive periodic

solutions associated with elements in $\Theta _{1}$, at least one positive

periodic solution associated with $\Gamma $ and none associated with $\Theta

_{2}$.

parameters is considered. It is shown that there are three mutually

exclusive and exhaustive subsets $\Theta _{1},\Gamma $ and $\Theta _{2}$ of

the parameter space such that there exist at least two positive periodic

solutions associated with elements in $\Theta _{1}$, at least one positive

periodic solution associated with $\Gamma $ and none associated with $\Theta

_{2}$.

#### Keywords

Positive periodic solution; coupled differential equations; monotone method; topological degree

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