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

TL;DR

This paper studies positive solutions to a supercritical elliptic equation on a Riemannian manifold that concentrate at submanifolds, providing existence results for certain types of manifolds including warped products.

Contribution

It establishes the existence of solutions concentrating at submanifolds for a class of supercritical elliptic equations on Riemannian manifolds, including warped products.

Findings

Existence of solutions concentrating at submanifolds.

Results apply to certain manifolds including warped products.

Provides new insights into supercritical elliptic equations on manifolds.

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.