Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 160, pp. 1-16.

Title: Effects of small spatial variation of the reproduction rate in a
       two species competition model

Authors: Georg Hetzer (Auburn Univ., AL, USA)
         Tung Nguyen (Univ. of Illinois, Springfield, IL, USA)
	 Wenxian Shen (Auburn Univ., AL, USA)

Abstract:
 Of concern is the effect of a small spatially inhomogeneous
 perturbation of the reproduction rate of the first species in a
 two-species Lotka-Volterra competition-diffusion problem with
 spatially homogeneous reaction terms. Apart from this perturbation
 and the diffusion rates, the two species are assumed to be identical.
 Our main result shows that the first species can always invade,
 whereas the second species can only invade under certain conditions
 which yield uniform persistence of both species. The proof relies on
 comparison techniques and properties of the principal eigenvalue
 of reaction-diffusion equations.
	 
Submitted December 9, 2009. Published November 05, 2010.
Math Subject Classifications: 35K57
Key Words: Lotka-Volterra two-species competition-diffusion system;
           nearly identical species; invasion; uniform persistence.