Abstract :
This paper is concerned with the existence of traveling wave fronts for delayed nonlocal
diffusion systems without quasimonotonicity, which can not be answered by the
known results. By using exponential order, upper–lower solutions and Schauder’s fixed
point theorem, we reduce the existence of monotone traveling wave fronts to the existence
of upper–lower solutions without the requirement of monotonicity. To illustrate our results,
we establish the existence of traveling wave fronts for two examples which are the
delayed non-local diffusion version of the Nicholson’s blowflies equation and the Belousov–
Zhabotinskii model. These results imply that the traveling wave fronts of the delayed
non-local diffusion systems without quasimonotonicity are persistent if the delay is small
