Radial and non-radial solutions to an elliptic problem on annular domains in Riemannian manifolds with radial symmetry

We show existence and uniqueness of positive radial solutions to{Delta(g)u + lambda u + u(p) = 0 in A u = 0 on partial derivative A,with lambda <0, A being an annular domain in a Riemannian manifold M of dimension n endowed with the metric dr(2) + S-2 (r)g(sn-1). Secondly we show that there exist positive non-radial solutions arising by bifurcation from the radial solution. p and lambda are the bifurcation parameters. (C) 2014 Elsevier Inc. All rights reserved.