Eigenfunctionals of Homogeneous Order-Preserving Maps with Applications to Sexually Reproducing Populations

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Abstract

Homogeneous bounded maps B on cones X+of ordered normed vector spaces X allow the definition of a cone spectral radius which is analogous to the spectral radius of a bounded linear operator. If X+is complete and B is also order-preserving, conditions are derived for B to have a homogeneous order-preserving eigenfunctional θ: X+→ R+associated with the cone spectral radius in analogy to one part of the Krein–Rutman theorem. Since homogeneous B arise as first order approximations at 0 of maps that describe the year-to-year development of sexually reproducing populations, these eigenfunctionals are an important ingredient in the persistence theory of structured populations with mating.

Original languageEnglish (US)
Pages (from-to)1115-1144
Number of pages30
JournalJournal of Dynamics and Differential Equations
Volume28
Issue number3-4
DOIs
StatePublished - Sep 1 2016

Keywords

  • Collatz–Wielandt numbers and bound
  • Concave map
  • Cone spectral radius
  • Eigenfunctional
  • Homogeneous map
  • Krein–Rutman type theorems
  • Mating functions
  • Order-preserving map

ASJC Scopus subject areas

  • Analysis

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