  In this paper, the positive solutions of a diffusive competition model with
saturation are mainly discussed. Under certain conditions, the stability and
multiplicities of coexistence states are analyzed. And by using the topological
degree theory in cones, it is proved that the problem has at least two positive
solutions under certain conditions. Finally, investigating the bifurcation of
coexistence states emanating from the semi-trivial solutions, some instability
and multiplicity results of coexistence state are expressed.
