Positive Steady-State Solutions of a Competing Reaction-Diffusion System with Large Cross-Diffusion Coefficients

This paper deals with a coupled system of reaction-diffusion equations modeling the competition of two species with cross diffusion. We discuss the existence of positive steady-state solutions in relation to the intrinsic birth rates a1, a2 of species and the cross diffusion coefficients b12 , b21. Our results show that positive steady-state solutions exist if a1 and a2 lie in certain range, or if b12 and b21 are sufficiently large.