Abstract

We establish the uniqueness of positive radial solutions of (equation presented) where A := Aa;b = fx 2 Rn : A < jxj < bg, 0 < a < b ≤ 1. We assume that the nonlinearity f ∈ C[0;1) ∩ C1(0;1) is such that f(0) = 0 and satisfies some convexity and growth conditions, and either f(s) > 0 for all s > 0, or has one zero at B > 0, is non positive and not identically 0 in (0;B) and it is positive in (B;1).