Principal spectral theory of time‐periodic nonlocal dispersal operators of Neumann type

In this communication, we prove some limits of the principal eigenvalue for nonlocal operator of Neumann type with respect to the parameters, which are significant in the understanding of dynamics of biological populations. We obtain a complete picture about limits of the principal eigenvalue in ter...

Full description

Saved in:
Bibliographic Details
Published in:Mathematische Nachrichten 2022-04, Vol.295 (4), p.806-826
Main Author: Vo, Hoang‐Hung
Format: Article
Language:English
Subjects:
Dispersion
Eigenvalues
generalized principal eigenvalue
Maximum principle
nonlocal Neumann operator
principal eigenvalue
Spectral theory
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this communication, we prove some limits of the principal eigenvalue for nonlocal operator of Neumann type with respect to the parameters, which are significant in the understanding of dynamics of biological populations. We obtain a complete picture about limits of the principal eigenvalue in term of the large and small dispersal rate and dispersal range classified by “Ecological Stable Strategy” of persistence. This solves some open problems remainning in the series of work [3, 32, 30], in which we have to overcome the new difficulties comparing to [3, 32, 30] since principal eigenvalue of a nonlocal Neumann operator is not monotone with respect to the domain. The maximum principle for this type of operator is also achieved in this paper.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201900474