The Picone identity: A device to get optimal uniqueness results and global dynamics in Population Dynamics. (August 2021)

• Record Type: Journal Article
• Authors: Fernández-Rincón, Sergio; López-Gómez, Julián
• Is Part Of: Nonlinear analysis. Volume 60(2021)
• Publication Date: 2021-08
• Subjects: Picone identity -- Superlinear indefinite problems -- Diffusive symbiotic models -- Diffusive competitive models -- Uniqueness of coexistence states -- Global dynamics; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103285
• Languages: English
• ISSNs: 1468-1218

Abstract

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.