Competing species equations with diffusion, large interactions, and jumping nonlinearities (Q1340454)

In this paper a reaction-diffusion system of the form \[ - \Delta u = au - u^ 2 - cuv, \quad - \Delta u = dv - v^ 2 - euv \quad \text{in} \quad D \subset \mathbb{R}^ n \] with homogeneous Dirichlet boundary conditions is studied. \(a,c,d,e\) are positive constants. The authors study the asymptotic behavior of the positive solution as the parameters \(c,e\) tend to infinity.