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Lotka–Volterra models with fractional diffusion

Published online by Cambridge University Press:  16 March 2017

Michele O. Alves
Affiliation:
Departamento de Matemática, Universidade Estadual de Londrina, 86057-970 Londrina – PR, Brazil ([email protected])
Marcos T. O. Pimenta
Affiliation:
Departamento de Matemática e Computação, Faculdade de Ciências e Tecnologia, Universidade Estadual Paulista, 19060-900 Presidente Prudente – SP, Brazil ([email protected])
Antonio Suárez
Affiliation:
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Faculdad de Matemáticas, Universidad de Sevilla, Calle Tarfia s/n, 41012 Sevilla, Spain ([email protected])

Extract

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.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2017 

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