On the Existence of Positive Periodic Solutions for N-Species Lotka-Volterra Competitive Systems with Distributed Delays and Impulses

摘要

In the present paper, we investigate the existence of positive periodic solutions for an n-species Lotka-Volterra system with distributed delays and nonlinear impulses. In the process, we convert the given system into an equivalent integral equation. Then, we construct appropriate mappings and use Krasnoselskii's fixed point theorem in a cone of a Banach space to show the existence of a positive periodic solution of the system. Easily verifiable sufficient conditions are established. We discuss our problem in two situations: when impulse functions are subquadratic and when they are sublinear. The technique to deal with the impulsive term is different from earlier approaches. In particular, the results improve some previous ones in the literature. Finally, an example is presented to illustrate the feasibility and effectiveness of the results.