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The number of solutions to an equation from catalysis*

Published online by Cambridge University Press:  14 November 2011

S. P. Hastings  and
J. B. McLeod
S. P. Hastings
Affiliation:
SUNY Center at Buffalo, Buffalo, NY 14214, U.S.A.
J. B. McLeod
Affiliation:
The Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB, England
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Synopsis

In catalysis theory there is interest in the number of solutions to the equation

with the boundary conditions

the parameters λ,β, γ being all positive and p a non-negative integer. The paper answers this question when γ is large, which is the interesting situation physically. Although the treatment is somewhat different in the cases p = 0 and p ≠ 0, the final answer is the same, that is, given β, there exist two positive functions λ1(γ) and λ2(γ) such that the problem has one solution if λ<λ1(γ), or λ>λ2(γ), three solutions if λ1(γ)<λ <λ2(γ), and two solutions if λ=λ1(γ) or λ=λ2(γ).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 101 , Issue 1-2 , 1985 , pp. 15 - 30
Copyright
Copyright © Royal Society of Edinburgh 1985

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References

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