Uniqueness of large solutions for non-monotone nonlinearities. (June 2019)

• Record Type: Journal Article
• Authors: López-Gómez, Julián; Maire, Luis
• Is Part Of: Nonlinear analysis. Volume 47(2019)
• Page Start: 291
• Page End: 305
• Publication Date: 2019-06
• Subjects: Large positive solutions -- Uniqueness -- Multiplicity -- Dynamical approach; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.11.003
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we construct a general class of non-monotone positive nonlinearities, f ( u ), for which the differential equation u ′ ′ = f ( u ) has a unique large solution in ( − T, T ) . In most of the available literature it is required f ( u ) to be strictly increasing in order to establish the uniqueness of the large solution.