On the existence and uniqueness of positive steady states in the volterra-lotka ecological models with diffusion

Using the theory of quasimonotone increasing systems developed by P. J. McKenna and W. Walter, we give a rather detailed analysis of the steady state solutions for the Volterra-Lotka model of two cooperating species, and prove some new nonexistence results for the competing species case. We indicate generalizations to the case of n > 2 species