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

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7 Scopus citations

Abstract

Homogeneous bounded maps B on cones (Formula presented.) 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 (Formula presented.) is complete and B is also order-preserving, conditions are derived for B to have a homogeneous order-preserving eigenfunctional (Formula presented.) 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)
JournalJournal of Dynamics and Differential Equations
DOIs
StateAccepted/In press - Jun 11 2015

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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