A Liouville theorem for a fourth order Hénon equation

We examine the following fourth order Hénon equation \label{pipe} Δ^2 u = |x|^αu^p \qquad \text{in}\ \IR^N, where $0 < α$. Define the Hardy-Sobolev exponent $p_4(α):= \frac{N+4 + 2 α}{N-4}$. We show that in dimension N=5 there are no positive bounded classical solutions of (\ref{pipe}) provided $1 < p < p_4(α)$.

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