In this note we discuss the radial positive solutions of

formula here

where D is the annulus {s∈Rn[ratio ]b<|s|<1}. Here 0<b<1, n[ges ]2, and g[ratio ]R→R is a suitable C1 function with g(0)[ges ]0 but with g changing sign. We answer a question on page 223 of the original Gidas–Ni–Nirenberg paper [8], by showing that the maximum of these solutions occurs at a point sε, where |sε|→b as ε→0. This also shows that the non-negativity condition in the result on page 223 of [8] is necessary.