A counterexample to a nonlinear version of the Kreĭn–Rutman theorem by R. Mahadevan. (June 2018)

• Record Type: Journal Article
• Authors: Arapostathis, Ari
• Is Part Of: Nonlinear analysis. Volume 171(2018)
• Page Start: 170
• Page End: 176
• Publication Date: 2018-06
• Subjects: primary 47H07 47H10 47J10 -- secondary 47B65; Kreĭn–Rutman theorem -- Positive operator -- Principal eigenvalue -- Convex cone; 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.2018.02.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this short note we present a simple counterexample to a nonlinear version of the Kreĭn–Rutman theorem reported in Mahadevan (2007). Correct versions of this theorem, and related results for superadditive maps are also presented.