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Existence of periodic positive solutions to nonlinear Lotka-Volterra competition

Benhadri Mimia, Caraballo Tomas, Zeghdoudi Halim

Opuscula Mathematica

2020

Vol. 40, no. 3

341--360

We investigate the existence of positive periodic solutions of a nonlinear Lotka-Volterra competition system with deviating arguments. The main tool we use to obtain our result is the Krasnoselskii fixed point theorem. In particular, this paper improves important and interesting work [X.H. Tang, X. Zhou, On positive periodic solution of Lotka-Volterra competition systems with deviating arguments, Proc. Amer. Math. Soc. 134 (2006), 2967-2974]. Moreover, as an application, we also exhibit some special cases of the system, which have been studied extensively in the literature.