Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 77, pp. 1-13.

Title: Sign-changing solutions of a fourth-order elliptic equation with
       supercritical exponent

Author: Kamal Ould Bouh (Taibah University, Saudi Arabia)

Abstract:
 In this article we study the nonlinear
 elliptic problem involving  nearly critical exponent
 $$\displaylines{
 \Delta^2 u = |u|^{8/(n-4)+\varepsilon}u\quad\text{in } \Omega, \cr
 \Delta u=u = 0\quad \text{on } \partial \Omega,
 }$$
 where $\Omega $ is a smooth bounded domain in $\mathbb{R}^n $ with
 $n \geq 5 $, and $\varepsilon$ is a positive parameter.
 We show that, for $\varepsilon$ small, there is no sign-changing solution
 with low energy which blow up at exactly two points.
 Moreover, we prove that this problem has no bubble-tower
 sign-changing solutions.

Submitted November 15, 2013. Published March 19, 2014.
Math Subject Classifications: 35J20, 35J60.
Key Words: Sign-changing solutions; critical exponent; bubble-tower solution.