STABLE COEXISTENCE IN THE VOLTERRA-LOTKA COMPETITION MODEL WITH DIFFUSION.

We study the existence, uniqueness, and stability of coexistence states in the Lotka-Volterra model with diffusion for two competing species. We assume that the parameters describing the interaction and self-limitation of the species are constant, and consider two types of growth and boundary conditions: periodic growth rates with Neumann boundary conditions, and constant growth rates with Dirichlet boundary conditions. The main tools for our investigations are existence and comparison theorems based on the maximum principle, upper and lower solutions, and the variational characterization of eigenvalues.