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Nonlocal problems arising from the birth-jump processes

Part of: Elliptic equations and systems Spectral theory and eigenvalue problems Mathematical biology in general

Published online by Cambridge University Press:  27 December 2018

M. Delgado ,
A. Suárez  and
I. B. M. Duarte
M. Delgado
Affiliation:
Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Fac. de Matemáticas, Univ. de Sevilla, C/. Tarfia s/n 41012, Sevilla, Spain (myj@us.es; suarez@us.es)
A. Suárez
Affiliation:
Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Fac. de Matemáticas, Univ. de Sevilla, C/. Tarfia s/n 41012, Sevilla, Spain (myj@us.es; suarez@us.es)
I. B. M. Duarte
Affiliation:
Universidade Federal do Pará, Faculdade de Matemática, CEP: 66075-110 Belém - Pa, Brazil (italobruno.mat@gmail.com)
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Abstract

In this paper, we prove the existence and uniqueness of a positive solution for a nonlocal logistic equation arising from the birth-jump processes. For this, we establish a sub-super solution method for nonlocal elliptic equations, we perform a study of the eigenvalue problems associated with these equations and we apply these results to the nonlocal logistic equation.

Keywords

birth-jump processesnonlocal elliptic equationsprincipal eigenvalue problemsub-super solution method

MSC classification

Primary: 35J60: Nonlinear elliptic equations 35P05: General topics in linear spectral theory
Secondary: 92B05: General biology and biomathematics
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 2 , April 2019 , pp. 447 - 469
Copyright
Copyright © Royal Society of Edinburgh 2018 

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