Existence and stability of coexistence states in a competition unstirred chemostat

In this paper, we consider the two similar competing species in a competition unstirred chemostat model with diffusion. The two competing species are assumed to be identical except for their maximal growth rates. In particular, we study the existence and stability of the coexistence states, and the semi-trivial equilibria or the unique coexistence state is the global attractor can be established under some suitable conditions. Our mathematical approach is based on Lyapunov-Schmidt reduction, the implicit function theory and spectral theory.