<oai_dc:dc xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
<dc:title>Asymptotic behavior of a fourth order mean field equation with Dirichlet boundary condition</dc:title>
<dc:creator>Frederic Robert</dc:creator><dc:creator>Juncheng Wei</dc:creator>
<dc:subject>35B40</dc:subject><dc:subject>35B45</dc:subject><dc:subject>35J40</dc:subject><dc:subject>asymptotic behavior</dc:subject><dc:subject>biharmonic equations</dc:subject>
<dc:description>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 $0 &lt; \rho \leq C$, we completely characterize the asymptotic behavior of the unbounded solutions.</dc:description>
<dc:publisher>Indiana University Mathematics Journal</dc:publisher>
<dc:date>2008</dc:date>
<dc:type>text</dc:type>
<dc:format>pdf</dc:format>
<dc:identifier>10.1512/iumj.2008.57.3324</dc:identifier>
<dc:source>10.1512/iumj.2008.57.3324</dc:source>
<dc:language>en</dc:language>
<dc:relation>Indiana Univ. Math. J. 57 (2008) 2039 - 2060</dc:relation>
<dc:coverage>state-of-the-art mathematics</dc:coverage>
<dc:rights>http://iumj.org/access/</dc:rights>
</oai_dc:dc>