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We consider asymptotic behavior of the following fourth order equation \[\Delta^2 u= \rho \frac{e^{u}}{\int_\Om e^{u} dx} {in} \Om, u= \partial_\nu u=0{on} \partial \Omega \] where $\Om$ is a smooth oriented bounded domain in$\R^4$. Assuming that $0<\rho \leq C$, we completely characterize theasymptotic behavior of the unbounded solutions.

Asymptotic behavior of a fourth order mean field equation with Dirichlet boundary condition