Existence of Traveling Waves of Lotka Volterra Type Models with Delayed Diffusion Term and Partial Quasimonotonicity

This paper is concerned with the existence of traveling wave solutions for diffusive two-species Lotka-Volterra systems with delay in both the reaction and diffusion terms without monotonicity. We extend the partial or cross monotone iteration method to systems that satisfy the partial quasi-monotone condition via construction appropriate upper and lower solutions. This is done by using Schauder’s fixed point theorem.