Boundary blow-up rate and uniqueness of the large solution for an elliptic cooperative system of logistic type. (February 2017)

• Record Type: Journal Article
• Authors: López-Gómez, Julián; Maire, Luis
• Is Part Of: Nonlinear analysis. Volume 33(2017)
• Page Start: 298
• Page End: 316
• Publication Date: 2017-02
• Subjects: Cooperative systems -- Large solutions -- Blowing-up rates -- Vanishing weights at variable rates -- Uniqueness; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.07.001
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper ascertains the blow-up rates of each of the components of a singular boundary value problem related to a cooperative system of logistic type, in order to establish the uniqueness of the large solution. Astonishingly, the cooperative coupling does not change the blow-up rates of the uncoupled system provided these blow-up rates are sufficiently close, though it changes exactly one of them, keeping invariant the other, when they are bounded away. This seems to be the first time where this change of behavior has been documented in the literature.