Solutions to a singularly perturbed supercritical elliptic equation on a Riemannian manifold concentrating at a submanifold

Abstract

Given a smooth Riemannian manifold (M,g)we investigate the existence of positive solutions to a singularly perturbed supercritical elliptic equation which concentrate at some submanifold of M. We obtain a posive answer for some manifolds, which include warped products.