Given a smooth Riemannian manifold (M, g) we investigate the existence of positive solutions to a supercritical singularly perturbed elliptic equation on M which concentrate at some submanifold of M as the singular parameter goes to 0. We obtain a positive answer for some manifolds, which include warped products.
Solutions to a singularly perturbed supercritical elliptic equation on a Riemannian manifold concentrating at a submanifold
GHIMENTI, MARCO GIPO;MICHELETTI, ANNA MARIA
2014-01-01
Abstract
Given a smooth Riemannian manifold (M, g) we investigate the existence of positive solutions to a supercritical singularly perturbed elliptic equation on M which concentrate at some submanifold of M as the singular parameter goes to 0. We obtain a positive answer for some manifolds, which include warped products.File in questo prodotto:
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