A counterexample to a nonlinear version of the Krein-Rutman theorem by R. Mahadevan
Ari Arapostathis
TL;DR
This paper provides a counterexample to a nonlinear extension of the Krein-Rutman theorem, clarifying the theorem's limitations and offering corrected versions and related results for superadditive maps.
Contribution
It presents a simple counterexample disproving a proposed nonlinear Krein-Rutman theorem and offers corrected formulations and related results for superadditive maps.
Findings
Counterexample invalidates the nonlinear Krein-Rutman theorem
Corrected versions of the theorem are provided
Related results for superadditive maps are discussed
Abstract
In this short note we present a simple counterexample to a nonlinear version of the Krein-Rutman theorem reported in [Nonlinear Anal. 11 (2007), 3084-3090]. Correct versions of this theorem, and related results for superadditive maps are also presented.
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