Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity

We consider positive solutions $u$ of the semilinear biharmonic equation ${\mathrm{\Delta }}^{2}u=\mathrm{\mid }x{\mathrm{\mid }}^{-\frac{n+4}{2}}g(\mathrm{\mid }x{\mathrm{\mid }}^{\frac{n-4}{2}}u)$ in $\mathbb R^n \setminus {0}$ with non-removable singularities at the origin. Under natural assumptions on the nonlinearity $g$, we show that $\mathrm{\mid }x{\mathrm{\mid }}^{\frac{n-4}{2}}u$ is a periodic function of $\ln \mathrm{\mid }x\mathrm{\mid }$ and we classify all such solutions.