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arXiv · 2607.24357

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

Luigi Appolloni·Serena Dipierro·Enrico Valdinoci
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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.

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Luigi Appolloni, Serena Dipierro, Enrico Valdinoci. 2026-07-27. A logistic equation with non-local operators of order near zero. https://arxiv.org/abs/2607.24357

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