Traveling wave solutions in [formula omitted]-dimensional delayed reaction–diffusion systems with mixed monotonicity

Abstract

This paper deals with the existence of traveling wave solutions for n-components delayed reaction–diffusion systems with mixed monotonicity. Based on a certain kind of mixed-quasimonotonicity reaction terms of higher dimension, we propose new conditions on the reaction terms and new definitions of upper and lower solutions. By using Schauder’s fixed point theorem and a cross-iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of upper and lower solutions. The general results obtained will be applied to type-K monotone diffusive Lotka–Volterra systems of higher dimension.