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Uniqueness, multiplicity and stability for positive solutions of a pair of reaction–diffusion equations

Published online by Cambridge University Press:  14 November 2011

Yihong Du
Affiliation:
Department of Mathematics, Statistics and Computing Science, University of New England, Armidale, NSW 2351, Australia

Abstract

We study the number and stability of the positive solutions of a reaction–diffusion equation pair. When certain parameters in the equations are large, the equation pair can be viewed as singular or regular perturbations of some single (or essentially single) equation problems, for which the number and stability of their solutions can be well understood. With the help of these simpler equations, we are able to obtain a rather complete understanding of the number and stability of the positive solutions for the equation pair for the cases that certain parameters are large. In particular, we obtain a fairly satisfactory description of the positive solution set of the equation pair.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1996

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