Solution components in a degenerate weighted BVP. (March 2020)

• Record Type: Journal Article
• Authors: Aleja, D.; Antón, I.; López-Gómez, J.
• Is Part Of: Nonlinear analysis. Volume 192(2020)
• Publication Date: 2020-03
• Subjects: primary 35K57 35B09 35J25; Generalized logistic equation -- Weighted problem -- Degenerate equation -- Non-classical mixed boundary conditions -- Structure of the positive solutions -- Counting the number of components; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111690
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper ascertains the structure of the set of positive solutions of a degenerate weighted logistic equation with a continuous kinetic under non-classical mixed boundary conditions. After establishing the uniqueness of the positive solution and the existence of two global components of positive solutions, it is shown that any component must be a continuous curve. Further, some general sufficient conditions are provided, in terms of the weight functions involved in the setting of the model, so that it possesses exactly two components of positive solutions. The problem of finding out the total number of components in the general case remains open.