A singular boundary value problem for a degenerate elliptic PDE. (June 2015)

• Record Type: Journal Article
• Authors: Biset, Tesfa; Mohammed, Ahmed
• Is Part Of: Nonlinear analysis. Volume 119(2015)
• Page Start: 222
• Page End: 234
• Publication Date: 2015-06
• Subjects: ∞-Laplacian -- Viscosity solution -- Principal eigenvalue and principal eigenfunction; 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.2014.09.028
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider a singular boundary value problem associated with the ∞ -Laplacian and having nonseparable inhomogeneous term. We establish the existence of ground state solutions to such a problem in bounded domains as well as in the whole Euclidean space. The investigation is based on subsolution and supersolution methods and existence of principal eigenfunctions to the eigenvalue problem of Dirichlet type corresponding to the ∞ -Laplacian.