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The Picone identity: A device to get optimal uniqueness results and global dynamics in Population Dynamics |
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| Affiliation: | 1. Departamento de Matemática, Universidade Federal de Santa Catarina, Campus Trindade, Florianópolis - SC, Brazil;2. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos - SP, Brazil;3. Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, Ponta Grossa - PR, Brazil |
| Abstract: | 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. |
| Keywords: | Picone identity Superlinear indefinite problems Diffusive symbiotic models Diffusive competitive models Uniqueness of coexistence states Global dynamics |
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