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nonlinear integral equations; monotone methods; population dynamics; positive solutions
In this paper we study the existence and uniqueness of positive and periodic solutions of nonlinear delay integral systems of the type $$ x(t) = \int_{t-\tau _1}^t f(s,x(s),y(s))\,ds $$ $$ y(t) = \int_{t-\tau _2}^t g(s,x(s),y(s))\,ds $$ which model population growth in a periodic environment when there is an interaction between two species. For the proofs, we develop an adequate method of sub-supersolutions which provides, in some cases, an iterative scheme converging to the solution.
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