Steady States In The Diffusive Volterra-Lotka Model For Several Competing Species (coexistence)

Existence, uniqueness, and stability of coexistence states in the diffusive Lotka-Volterra model for several species are studied. It is assumed that the parameters describing the interaction and self limitation of the species are positive constants. We consider boundary value problems involving equal or unequal growth rates. Periodic growth and interaction rates are considered for existence of periodic solutions. Conditions are determined for the existence, uniqueness, and stability of coexistence states.The main tools of investigation are the method of upper and lower solutions, maximum principles, Lyapunov functions, and the variational characterization of eigenvalues.