Traveling wave solutions in delayed reaction–diffusion systems with mixed monotonicity

✍ Scribed by Qi-Ru Wang; Kai Zhou

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 937 KB
• Volume: 233
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2009.11.002

✦ Synopsis

Lotka-Volterra system a b s t r a c t This paper deals with the existence of traveling wave solutions in delayed reactiondiffusion systems with mixed monotonicity. Based on two different mixed-quasi monotonicity reaction terms, 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 new 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 have been applied to type-K monotone and type-K competitive diffusive Lotka-Volterra systems.