On stationary solutions to reaction-diffusion equations with nonlocal term

TL;DR

This paper establishes the existence of radial stationary solutions for certain nonlocal reaction-diffusion equations, relevant to models like self-gravitating particles, expanding understanding of their mathematical properties.

Contribution

It provides new existence results for radial solutions to elliptic nonlocal problems derived from reaction-diffusion models, particularly in the context of self-gravitating systems.

Findings

Existence of radial solutions demonstrated.

Applicable to models of self-gravitating particles.

Advances understanding of nonlocal reaction-diffusion equations.

Abstract

In this paper we obtain the existence of a radial solution for some elliptic nonlocal problem with constraints. The problem arises from some reaction-diffusion equation modelling among others system of self-gravitating particles when one looks for its stationary solutions.