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

Wenjing Chen; Xiaomeng Huang

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arXiv · 2202.06006

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

Wenjing Chen·Xiaomeng Huang

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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 $Ω$ is an open bounded domain in $\mathbb{R}^N$, $N\geq 5$, and $B(ξ_0,\varepsilon)$ is a ball centered at $ξ_0$ with radius $\varepsilon$, $\varepsilon$ 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.

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Wenjing Chen, Xiaomeng Huang. 2022-02-12. Sign-changing bubble tower solutions for a Paneitz-type problem. https://arxiv.org/abs/2202.06006

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