Asymptotic behavior of a fourth order mean field equation with Dirichlet boundary condition Frederic RobertJuncheng Wei 35B4035B4535J40asymptotic behaviorbiharmonic equations We consider asymptotic behavior of the following fourth order equation \[ \Delta^{2}u = \rho \frac{e^{u}}{\displaystyle\int_{\Omega} e^{u}\,\mathrm{d}x} \mbox{ in } \Omega, \quad u = \partial_{\nu} u = 0 \mbox{ on } \partial\Omega \] where $\Omega$ is a smooth oriented bounded domain in $\mathbb{R}^{4}$. Assuming that $0 < \rho \leq C$, we completely characterize the asymptotic behavior of the unbounded solutions. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3324 10.1512/iumj.2008.57.3324 en Indiana Univ. Math. J. 57 (2008) 2039 - 2060 state-of-the-art mathematics http://iumj.org/access/