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Lotka–Volterra models with fractional diffusion

Part of: Elliptic equations and systems Qualitative behavior Mathematical biology in general

Published online by Cambridge University Press:  16 March 2017

Michele O. Alves ,
Marcos T. O. Pimenta  and
Antonio Suárez
Michele O. Alves
Affiliation:
Departamento de Matemática, Universidade Estadual de Londrina, 86057-970 Londrina – PR, Brazil (michelealves@uel.br)
Marcos T. O. Pimenta
Affiliation:
Departamento de Matemática e Computação, Faculdade de Ciências e Tecnologia, Universidade Estadual Paulista, 19060-900 Presidente Prudente – SP, Brazil (pimenta@fct.unesp.br)
Antonio Suárez
Affiliation:
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Faculdad de Matemáticas, Universidad de Sevilla, Calle Tarfia s/n, 41012 Sevilla, Spain (suarez@us.es)
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We study Lotka–Volterra models with fractional Laplacian. To do this we study in detail the logistic problem and show that the sub–supersolution method works for both the scalar problem and for systems. We apply this method to show the existence and non-existence of positive solutions in terms of the system parameters.

Keywords

fractional LaplacianLotka–Volterra modelssub–supersolution method

MSC classification

Secondary: 35J25: Boundary value problems for second-order elliptic equations 45M20: Positive solutions 92B05: General biology and biomathematics
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 3 , June 2017 , pp. 505 - 528
Copyright
Copyright © Royal Society of Edinburgh 2017