Existence and asymptotic behavior of invasion wave solutions in temporally discrete diffusion systems with delays

Abstract

This paper is concerned with the existence and asymptotic behavior of invasion wave solutions for a time-discrete delayed diffusion competitive system with non-quasi-monotone conditions. The existence of invasion wave solution is investigated by applying upper–lower solutions method and Schauder’s fixed point theorem. Further, with the help of Ikeharaś theorem, we establish the exponential decay asymptotic behavior of traveling wave solutions at the minus/plus infinity.