A variational inequality theory in reflexive smooth Banach spaces and applications to p-Laplacian elliptic inequalities. (January 2015)

• Record Type: Journal Article
• Authors: Lan, Kunquan
• Is Part Of: Nonlinear analysis. Volume 113(2015)
• Page Start: 71
• Page End: 86
• Publication Date: 2015-01
• Subjects: primary 49J40 -- secondary 35R45 47J20 47H05 47H06 92D25; Variational inequality -- Demicontinuous S-contractive map -- Essential map -- Reflexive smooth Banach space -- p-Laplacian elliptic inequality -- Nonzero positive weak solution -- First eigenvalue; 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.2014.10.002
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We develop a theory of variational inequality for demicontinuous S -contractive maps in reflexive smooth Banach spaces. Variational inequality theorems are proved and applied to study existence of nonzero positive weak solutions for p -Laplacian elliptic inequalities and a population model of one species arising in mathematical biology.