The Frontiers of Society, Science and Technology, 2020, 2(1); doi: 10.25236/FSST.2020.020117.
College of Sciences, North University of China, Taiyuan, Shanxi 030051, China
This paper is concerned with the monotone traveling wave solutions for a diffusive Lotka-Volterra weak competitive system with delays. Using the method of upper-lower solutions, necessary and sufficient conditions are established for the existence and nonexistence of monotone traveling wave solutions connecting the trivial steady state with the coexistence steady state of weak competitive system.
Traveling waves; Monotone; Delays; Weak competition system
Linhong Yao. Monotone Traveling Waves of a Diffusive Lotka-Volterra Weak Competitive System with Delays. The Frontiers of Society, Science and Technology (2020) Vol. 2 Issue 1: 122-130. https://doi.org/10.25236/FSST.2020.020117.
 J Fang, J Wu (2012), Monotone traveling waves for delayed Lotka-Volterra competition systems, Discrete Contin. Dyn. Syst, no.32, pp.3043-3058.
 W T Li, G Lin, S Ruan (2006). Existence of traveling wave solutions in delayed reaction diﬀusion systems with application to diﬀusion-competition systems, Nonlinearity, no.19, pp.1253-73.
 G Y Lv, M X Wang (2010), Traveling wave front in diﬀusive and competitive Lotka-Volterra system with delays, Nonlinear Anal, no.11, pp.1323-29.
 Jan H, Van Vuuren (1995). The existence of traveling plane waves in a general class of competition Cdiﬀusion systems, IMA J. Appl. Math, no.55, pp. 135-48.
 Y Wang, X Li (2018). Entire solutions for the classical competitive Lotka-Volterra system with diﬀusion in the weak competition case, Nonlinear Analysis (RWA), no.42, pp.1-23.
 H Y Wang (2011). Spreading speeds and traveling waves for non-cooperative reaction-diﬀusion systems, J. Nonlinear Science, no.21, pp. 747-783.
 W J Ni, J P Shi, M X Wang (2018). Global stability and pattern formation in a nonlocal diﬀusive Lotka-Volterra competition model, J. Diﬀerential Equations, no.264, pp. 6891-6932.
 T R Zhang, W D Wang, K F Wang (2016). Minimal wave speed for a class of non-cooperative diﬀusion-reaction system, J.Diﬀerential Equations, pp. 2763-2791.
 L H Yao, R Yuan, Existence of traveling wavefronts for a delayed competitive diﬀusion diﬀusion system, submitted.