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Given a Riemannian compact manifold (M,g) of dimension n>4, we have proven in[1] under some conditions that the equation : Pg(u) = Bu +Au2+Cu (1) where Pgis the GJMS-operator, n = dim(M) > 2k, A, B and C are smooth positive functionson M, p > 1 and 2] denotes the critical Sobolev admits twodistinct positivesolutions. The proof of this result is essentially based on the given smoothfunction ' > 0 with norm k'kPg = 1 fulfilling some conditions ( see Theorem 3in [1]). In this note we construct an example of such function on the unitstandard sphere (Sn; h). Con- sequently the conditions of the Theorem areimproved in the case of (Sn; h)

Singular elliptic equation involving the GJMS operator on the standard unit sphere