一类时间周期的时滞竞争系统行波解的存在性

Abstract

A time-periodic reaction-diffusion Lotka-Volterra competition model with delay was considered. Under certain conditions, with the method of super- and sub-solutions and monotone iterations, the existence of time-periodic traveling waves connecting 2 semi-trivial periodic solutions of the corresponding kinetic system was proved with wave speed c*.Furthermore, the traveling wave solutions for c* were proved to be monotone with the comparison principle, and the asymptotic behaviors of traveling wave solutions were obtained at minus/plus infinity. Finally, the existence of traveling wave solutions was proved at wave speed c=c^*.