Traveling wave solutions in delayed diffusion systems via a cross iteration scheme

This paper is concerned with the existence of traveling wave solutions for delayed reaction diffusion systems which contain the competition diffusion systems with time lags. By using a cross iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of admissible upper and lower solutions, which also provides a constructive process of the traveling wave solutions. To illustrate our conclusion, we consider a delayed diffusion system with the Gilpin–Ayala type nonlinearity and establish the existence of its traveling wave solutions, which cannot be answered by the existing results.