Uniqueness of positive radial solutions of superlinear elliptic equations in annuli

Abstract We present a generalized comparison identity for a two point boundary value problem, and we apply it to show the uniqueness of positive radial solutions of { Δ u ( x ) + f ( u ( x ) ) = 0 in  A a , b , u ( x ) = 0 on  ∂ A a , b , where n ∈ N with n ≥ 2 , 0 a b ∞ , A a , b = { x ∈ R N : a | x | b } and f ∈ C 1 [ 0 , ∞ ) is a superlinear function.

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