A logistic equation with non-local operators of order near zero

Luigi Appolloni; Serena Dipierro; Enrico Valdinoci

A logistic equation with non-local operators of order near zero

Analysis of PDEs 2026-07-27 v1

Authors: Luigi Appolloni , Serena Dipierro , Enrico Valdinoci

Abstract

In this paper we study an equation driven by a non-local operator of order "near zero" with mixed Dirichlet-Neumann boundary conditions, modelling a biological system consisting of a population self-competing for resources in a closed environment and subject to an extremely heavy-tailed dispersal process. We establish several results concerning the existence of states in which the population can survive requiring different assumptions on the non-linear reaction term and on the various configurations of the sets where the Dirichlet or Neumann conditions hold.

Keywords

logistic equation nonlocal operator mixed boundary condition dirichlet-neumann population model existence of solutions

Cite

@article{arxiv.2607.24357,
  title  = {A logistic equation with non-local operators of order near zero},
  author = {Luigi Appolloni and Serena Dipierro and Enrico Valdinoci},
  journal= {arXiv preprint arXiv:2607.24357},
  year   = {2026}
}

Comments

28 pages, comments welcome