Sign-changing bubble tower solutions for a Paneitz-type problem

This paper is concerned with the following biharmonic problem

$\begin{cases} \Delta^2 u = |u|^{\frac{8}{N-4}}u &\text{in } \ \Omega\backslash \overline{{B\left(\xi_0,\varepsilon\right)}},\\ u = \Delta u = 0 &\text{on } \ \partial \left(\Omega \backslash \overline{{B\left(\xi_0,\varepsilon\right)}}\right), \end{cases}\quad\quad\text{(0.1)}$

where Ω is an open bounded domain in $\mathbb{R}^N$, $N\unicode{x2A7E} 5$, and $B(\xi_0,\varepsilon)$ is a ball centered at ξ₀ with radius ɛ, ɛ is a small positive parameter. We obtain the existence of solutions for problem (0.1), which is an arbitrary large number of sign-changing solutions whose profile is a superposition of bubbles with alternate sign which concentrate at the centre of the hole.