A sharp Sobolev inequality and its applications to an indefinite elliptic equation with Neumann boundary conditions. (August 2020)

• Record Type: Journal Article
• Authors: de Souza, Manassés; Felix, Diego D.; de Medeiros, Everaldo S.
• Is Part Of: Nonlinear analysis. Volume 197(2020)
• Publication Date: 2020-08
• Subjects: primary 35J20 -- secondary 35B25 35B40 35J65; Nonlinear elliptic problems -- Neumann boundary value problems -- Upper half-space -- Variational methods; 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.2020.111840
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we prove a sharp weighted Sobolev inequality on the upper half-space. As a consequence of this inequality we derive some existence, nonexistence and multiplicity results to a class of indefinite semilinear elliptic equations with Neumann boundary conditions.