Geodesic
Systems of nonlinear delay integral equations modelling population growth in a periodic environment
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 4, pp. 633-644.

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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.
Classification : 34K15, 45G10, 45G15, 45M15, 45M20, 92D25
Keywords: nonlinear integral equations; monotone methods; population dynamics; positive solutions 
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     title = {Systems of nonlinear delay integral equations modelling population growth  in a periodic environment},
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Cañada, A.; Zertiti, A. Systems of nonlinear delay integral equations modelling population growth  in a periodic environment. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 4, pp. 633-644. http://geodesic.mathdoc.fr/item/CMUC_1994__35_4_a4/