Existence of positive solutions can be proved by upper-lower solution, monotone iteration, bifurcation and degree theory. In this talk we illustrate the proof by means of the degree theory method of cone index. We consider a prey-predator or competing species model with homogeneous (hostile) Dirichlet boundary data. The method expresses the condition for coexistence in terms of the principal eigenvalues of some related scalar linear equations. From these conditions one can readily see how coexistence depends on the relationship between the size of the environment domain, species growth and interaction rates.