On a Fourth Order Lichnerowicz Type Equation Involving The Paneitz-Branson Operator

TL;DR

This paper investigates fourth-order singular critical equations related to the Paneitz-Branson operator, establishing conditions for their existence and non-existence, contributing to the understanding of higher-order conformally invariant equations.

Contribution

It introduces new existence and non-existence results for a class of fourth-order Lichnerowicz type equations involving the Paneitz-Branson operator.

Findings

Proved existence of solutions under certain conditions.

Established non-existence results in specific scenarios.

Enhanced understanding of singular critical equations involving higher-order operators.

Abstract

In this paper, we study some fourth order singular critical equations of Lichnerowicz type involving the Paneitz-Branson operator, and we prove existence and non existence results under given assumptions.