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This paper is concerned with the traveling wave solutions of delayedreaction-diffusion systems. By using Schauder's fixed point theorem, theexistence of traveling wave solutions is reduced to the existence ofgeneralized upper and lower solutions. Using the technique of contractingrectangles, the asymptotic behavior of traveling wave solutions for delayeddiffusive systems is obtained. To illustrate our main results, the existence,nonexistence and asymptotic behavior of positive traveling wave solutions ofdiffusive Lotka-Volterra competition systems with distributed delays areestablished. The existence of nonmonotone traveling wave solutions of diffusiveLotka-Volterra competition systems is also discussed. In particular, it isproved that if there exists instantaneous self-limitation effect, then thelarge delays appearing in the intra-specific competitive terms may not affectthe existence and asymptotic behavior of traveling wave solutions.

Traveling Wave Solutions for Delayed Reaction-Diffusion Systems and  Applications to Lotka-Volterra Competition-Diffusion Models with Distributed  Delays