Perron Theorem in the monotone iteration method for traveling waves in delayed reaction–diffusion equations

In this paper we revisit the existence of traveling waves for delayed reaction–diffusion equations by the monotone iteration method. We show that Perron Theorem on existence of bounded solution provides a rigorous and constructive framework to find traveling wave solutions of reaction–diffusion systems with time delay. The method is tried out on two classical examples with delay: the predator–prey and Belousov–Zhabotinskii models.