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This paper infers from a generalized Picone identity the uniqueness of thestable positive solution for a class of semilinear equations of superlinearindefinite type, as well as the uniqueness and global attractivity of thecoexistence state in two generalized diffusive prototypes of the symbiotic andcompeting species models of Lotka-Volterra. The optimality of these uniquenesstheorems reveals the tremendous strength of the Picone identity.

The Picone identity: A device to get optimal uniqueness results and global dynamics in Population Dynamics