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 language | English (US) |
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Pages (from-to) | 1115-1144 |
Number of pages | 30 |
Journal | Journal of Dynamics and Differential Equations |
Volume | 28 |
Issue number | 3-4 |
DOIs | |
State | Published - 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