Abstract:In this paper we study the existence and uniqueness of positive and periodic solutions of nonlinear delay integral systems of the type $$ \gather x(t) = \int _{t-\tau _1}^t f(s,x(s),y(s)) ds y(t) = \int _{t-\tau _2}^t g(s,x(s),y(s)) ds \endgather $$ 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.
Keywords: nonlinear integral equations, monotone methods, population dynamics, positive solutions
AMS Subject Classification: 45G15, 92D25, 45M15