On the existence of positive periodic solutions for n−species Lotka-Volterra competitive systems with distributed delays and impulses

Abstract

In this paper, we investigate the existence of positive periodic solutions for an n-species Lotka-Volterra system with distributed delays and impulsive effect. In the process we use integrating factors and convert the given Lotka-Volterra differential equation into an equivalent integral equation. Then we construct appropriate mappings and use Krasnoselskii’s fixed point theorem to show the existence of a positive periodic solution of this system. In particular, the results improve some previous ones in the literature. Finally, as an application, we exhibit an example to illustrate the effectiveness of our abstract results