Abstract
We consider the biharmonic equation with supercritical nonlinearity (P-epsilon) : Delta(2)u = K 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, K is a C-3 positive function, and epsilon is a positive real parameter. In contrast with the subcritical case, we prove the nonexistence of sign-changing solutions of (P-epsilon) that blow up at two near points. We also show that (P-epsilon) has no bubble-tower sign-changing solutions.