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.