## Differential and Integral Equations

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

### A Paneitz-type problem in pierced domains

S. Alarcón and A. Pistoia

#### Abstract

We study the critical problem \begin{equation} \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$_\varepsilon$} \end{equation} 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

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1431347865

**Mathematical Reviews number (MathSciNet)**

MR3345335

**Zentralblatt MATH identifier**

1363.35103

**Subjects**

Primary: 35J30: Higher-order elliptic equations [See also 31A30, 31B30] 35B25: Singular perturbations 35J35: Variational methods for higher-order elliptic equations 35J91: Semilinear elliptic equations with Laplacian, bi-Laplacian or poly- Laplacian

#### Citation

Alarcón, S.; Pistoia, A. A Paneitz-type problem in pierced domains. Differential Integral Equations 28 (2015), no. 7/8, 823--838. https://projecteuclid.org/euclid.die/1431347865