IJPAM: Volume 55, No. 3 (2009)

EXISTENCE OF TRAVELING WAVES IN LOTKA-VOLTERRA
COMPETITION MODELS WITH DISTRIBUTED
MATURATION DELAY

Ren-Hu Wang$^1$, Zhang Fei-Yu$^2$, Xing-Xue Yan$^3$
$^{1,2,3}$Department of Mathematics
Hexi University
Zhangye, Gansu, 734000, P.R. CHINA
$^1$e-mail: wangrh03@lzu.cn


Abstract.This paper is concerned with a Lotka-Volterra competition model with distributed maturation delays. The stability of uniform steady states are firstly studied by investigating the eigenvalues of the linearization in every equilibrium and then, the existence of traveling wave solution connecting two boundary equilibriums is established by using monotone iteration together with upper and lower solutions method when the coexistence equilibrium absents. The results presented in this paper expand a number of existing ones.

Received: December 23, 2008

AMS Subject Classification: 26A33

Key Words and Phrases: time-delay, nonlocal, traveling waves, stage-structured, competitive models

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 3