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

Abstract

This paper is concerned with the following biharmonic problem \begin{equation}\label{ineq} \begin{cases} Δ^2 u=|u|^{\frac{8}{N-4}}u &\text{ in } \ Ω\backslash \overline{B(ξ_0,\varepsilon)}, u=Δu=0 &\text{ on } \ \partial (Ω\backslash \overline{B(ξ_0,\varepsilon)}), \end{cases} \end{equation} where $\Omega$ is an open bounded domain in ${\mathbb{R}}^N$, $N\ge 5$, and $B({\xi }_0,\epsilon )$ is a ball centered at ${\xi }_0$ with radius $\epsilon$, $\epsilon$ is a small positive parameter. We obtain the existence of solutions for problem (\ref{ineq}), which is an arbitrary large number of sign-changing solutions whose profile is a superposition of bubbles with alternate sign which concentrate at the center of the hole.

arXiv admin note: text overlap with arXiv:1710.01880 by other authors