## Differential and Integral Equations

### A Paneitz-type problem in pierced domains

#### Abstract

We study the critical problem $$\left\{ \begin{array}{ll} \Delta ^{2}u=u^{\frac{N+4}{N-4} } & \mbox{ in }\Omega\setminus \overline{B(\xi_0,\varepsilon) }, \\ u>0 & \mbox{ in }\Omega\setminus \overline{B(\xi_0,\varepsilon) }, \\ u=\Delta u=0 & \mbox{ on }\partial (\Omega \setminus \overline{B(\xi_0,\varepsilon) }), \end{array} \right. \tag{P_\varepsilon}$$ where $\Omega$ is an open bounded domain in $\mathbb{R}^N$, $N\ge5$, $\xi_0\in\Omega$ and $B(\xi_0,\varepsilon)$ is the ball centered at $\xi_0$ with radius $\varepsilon>0$ small enough. We construct solutions of (P$_\varepsilon$) blowing-up at the center of the hole as the size of the hole goes to zero.

#### Article information

Source
Differential Integral Equations, Volume 28, Number 7/8 (2015), 823-838.

Dates
First available in Project Euclid: 11 May 2015