On a Paneitz-type equation in six-dimensional domains

Abstract

In this paper, we consider the equation $\Delta ^2 u=K u^5$, $u>0$ in $\Omega$, $u=\Delta u=0$ on $\partial\Omega$, where $K$ is a positive function and $\Omega$ is a bounded and smooth domain in $\mathbb R^6$. Using the theory of critical points at infinity, we give some topological conditions on $K$ to ensure some existence results.