Travelling wave fronts in reaction–diffusion systems with spatio-temporal delays

This paper deals with the existence of travelling wave fronts in reaction–diffusion systems with spatio-temporal delays. Our approach is to use monotone iterations and a nonstandard ordering for the set of profiles of the corresponding wave system. New iterative techniques are established for a class of integral operators when the reaction term satisfies different monotonicity conditions. Following this, the existence of travelling wave fronts for reaction–diffusion systems with spatio-temporal delays is established. Finally, we apply the main results to a single-species diffusive model with spatio-temporal delay and obtain some existence criteria of travelling wave fronts by choosing different kernels.