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

Abstract

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.