New results on positive periodic solutions of a periodic integro-differential competition system
The author considers a system of integro-differential equations with infinite delay of convolution type. These equations may be used in mathematical models from ecology for populations and therefore one is interested in positive solutions. Many populations undergo periodic changes and therefore the focus of this paper is on the existence of positive periodic solutions. After the usual preliminaries, the main part of the paper is the proof of Theorem 3. This theorem gives conditions guaranteeing that the equation has at least one periodic positive solution. Finally the authors give a condition that ensures that the periodic solution is globally asymptotically stable.
system of integro-differential equations
positive solution, periodic solution, infinite delay
scientific article; zbMATH DE number 2082071