The existence of minimal large positive solutions for a class of nonlinear cooperative systems. (December 2022)

• Record Type: Journal Article
• Authors: López-Gómez, Julián; Maire, Luis
• Is Part Of: Nonlinear analysis. Volume 68(2022)
• Publication Date: 2022-12
• Subjects: Nonlinear cooperative systems -- Large solution -- Large supersolution -- Minimal large solution; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103693
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we establish the existence of the minimal large positive solution for a general class of nonlinear cooperative systems including the simplest prototype of García-Melián et al. (2016). Precisely, based on the existence of a large positive supersolution, we can infer the existence of the minimal large positive solution. Moreover, we also give some sufficient easily computable conditions for the existence of a large positive supersolution. Our results generalize, very substantially, some of the findings of García-Melián et al. (2016) adopting a rather novel methodology.