Singular elliptic equation involving the GJMS operator on compact Riemannian manifold

TL;DR

This paper investigates a singular elliptic equation involving the GJMS operator on compact Riemannian manifolds, establishing conditions for multiple solutions and nonexistence.

Contribution

It introduces new multiplicity and nonexistence results for singular elliptic equations with the GJMS operator on compact manifolds.

Findings

Established multiplicity of solutions under certain conditions

Proved nonexistence results in specific cases

Extended understanding of elliptic equations involving higher-order operators

Abstract

In this paper we consider a singular elliptic equation involving the GJMS (Graham-Jenne-Mason-Sparling) operator of order k on n-dimensional compact Riemannian manifold with 2k<n. Mutiplicity and nonexistence results are established.