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+λu+u^p=0 in A,u=0 on ∂A, with λ. < 0, A being an annular domain in a Riemannian manifold M of dimension n endowed with the metric dr^2+S^2(r)g_(S^n-1). Secondly we show that there exist positive non-radial solutions arising by bifurcation from the radial solution. p and λ are the bifurcation parameters.