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
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10.1512/iumj.2008.57.3324
10.1512/iumj.2008.57.3324
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Indiana Univ. Math. J. 57 (2008) 2039 - 2060
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