On a Paneitz Type Equation in Six Dimensional Domains

TL;DR

This paper investigates a fourth-order PDE with critical Sobolev exponent in six-dimensional domains, applying critical point theory at infinity to establish existence results based on topological conditions.

Contribution

It introduces new topological criteria for the existence of solutions to a Paneitz-type equation in six dimensions, expanding the application of critical point theory at infinity.

Findings

Existence of solutions under specific topological conditions

Application of critical points at infinity to fourth-order PDEs

Topological methods extend to six-dimensional critical Sobolev problems

Abstract

In this paper we consider a fourth order equation involving the critical Sobolev exponent on a bounded and smooth domain in $\R^6$. Using theory of critical points at infinity, we give some topological conditions on a given function defined on a domain to ensure some existence results.