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A general monotone scheme for elliptic systems with applications to ecological models

Published online by Cambridge University Press:  14 November 2011

Philip Korman  and
Anthony W. Leung
Philip Korman
Affiliation:
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221, U.S.A.
Anthony W. Leung
Affiliation:
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221, U.S.A.
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Synopsis

We consider weakly-coupled elliptic systems of the type

with each fi being either an increasing or a decreasing function of each uj. Assuming the existence of coupled super- and subsolutions, we prove the existence of solutions, and provide a constructive iteration scheme to approximate the solutions. We then apply our results to study the steady-states of two-species interaction in the Volterra–Lotka model with diffusion.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 102 , Issue 3-4 , 1986 , pp. 315 - 325
Copyright
Copyright © Royal Society of Edinburgh 1986

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