# Multiple solutions of an elliptic Hardy-Sobolev equation with critical exponents on compact Riemannian manifolds

## TL;DR

This paper establishes the existence of multiple solutions to a critical elliptic equation involving Hardy potential on compact Riemannian manifolds, advancing understanding of nonlinear PDEs with critical exponents.

## Contribution

It proves the existence of multiple solutions for an elliptic Hardy-Sobolev equation with critical exponents on compact Riemannian manifolds, a novel result in geometric analysis.

## Key findings

- Multiple solutions are proven to exist.
- The results extend known theory to Hardy-Sobolev equations.
- The work applies variational methods on manifolds.

## Abstract

On a compact Riemannian manifold, we prove the existence of multiple solutions for an elliptic equation with critical Sobolev growth and critical Hardy potential.