Coexistence in the Competition Model with Diffusion

In this paper we study positive steady-state solutions of a reaction-diffusion model, the Lotka-Volterra competition system, under homogeneous Dirichlet boundary conditions. We extend previous results on existence and nonuniqueness of coexistence solutions to larger areas of parameter space. The techniques we use are multiparameter bifurcation theory, variational inequalities, and elliptic theory.