  This paper infers from a generalized Picone identity the uniqueness of the
stable positive solution for a class of semilinear equations of superlinear
indefinite type, as well as the uniqueness and global attractivity of the
coexistence state in two generalized diffusive prototypes of the symbiotic and
competing species models of Lotka-Volterra. The optimality of these uniqueness
theorems reveals the tremendous strength of the Picone identity.
