On a fourth order elliptic equation with supercritical exponent

This paper is concerned with the semi-linear elliptic problem involving nearly critical exponent (P-epsilon): Delta(2)u = vertical bar u vertical bar(8/(n-4)+epsilon) u in Omega, Delta u = u = 0 on partial derivative Omega, where Omega is a smooth bounded domain in R-n, n >= 5, and epsilon is a positive real parameter. We show that, for epsilon small, (P-epsilon) has no sign-changing solutions with low energy which blow up at exactly three points. Moreover, we prove that (P-epsilon) has no bubble-tower sign-changing solutions.