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Uniqueness of positive radial solutions of a semilinear Dirichlet problem in an annulus

Published online by Cambridge University Press:  11 July 2007

S. L. Yadava
S. L. Yadava
Affiliation:
TIFR Centre, PO Box 1234, Bangaloe 560 012, India ([email protected])
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Abstract

We establish the uniqueness of positive radial solutions of −Δu = up − u in B(R1, R2), u = 0 on ∂B(R1, R2), where B(R1, R2) is an annulus and 0 < R1 < R2 ≤ ∞, in the following cases.

(a) n ∈ {3, 4} and 1 < p ≤ n/(n − 2).

(b) n ∈ {5, 6, 7, 8} and 1 < p ≤ p0(n) for some p0(n) < n/(n − 2).

Earlier to this result, the uniqueness has been obtained by Coffman for n = 3 and 1 < p ≤ 3 and by Yadava for p ≥ (n + 2)/(n − 2) and n ≥ 3.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 130 , Issue 6 , December 2000 , pp. 1417 - 1428
Copyright
Copyright © Royal Society of Edinburgh 2000

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