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lotka–volterra models

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Lotka–Volterra models with fractional diffusion
Part of
Michele O. Alves, Marcos T. O. Pimenta, Antonio Suárez
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 147 / Issue 3 / June 2017

Published online by Cambridge University Press:

16 March 2017, pp. 505-528

Print publication:

June 2017
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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.