Traveling wavefronts for a Lotka–Volterra system of type-[formula omitted] with delays

Abstract

We deal with the existence of traveling wavefronts of a 3-dimensional Lotka–Volterra system of type-K with delays, connecting either two boundary steady states or one boundary steady state and one positive steady state, which ecologically means a successful invasion of the first and second species. Our contribution here is mainly the construction and verification of upper–lower solutions. We further show that such a form of upper–lower solutions can be also served as the upper–lower solutions of the n-dimensional Lotka–Voterral cooperative system with delays. We also obtain a larger range of wave speed for the system than present in the existing literature.