2019/10/29 by Hoang‐Hung Vo, Vo, Hoang-Hung
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1911.06119
openalex publication_date 2019/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this communication, we prove some important 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 obtained 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, 28, 29], in which we have to overcome the new difficulties comparing to [3, 28, 29] since principal eigenvalue of 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.