Single Blow up Solutions for a Slightly Subcritical Biharmonic Equation
| dc.creator | Mehdi, Khalil El | |
| dc.date | 2004-12-06 | |
| dc.date.accessioned | 2026-07-07T05:14:58Z | |
| dc.date.available | 2026-07-07T05:14:58Z | |
| dc.description | In this paper, we consider a biharmonic equation under the Navier boundary condition and with a nearly critical exponent $(P_ε): Δ^2u=u^{9-ε}, u>0$ in $Ω$ and $u=Δu=0$ on $\partialΩ$, where $Ω$ is a smooth bounded domain in $\R^5$ and $ε>0$. We study the asymptotic behavior of solutions of $(P_ε)$ which are minimizing for the Sobolev qutient as $ε$ goes to zero. We show that such solutions concentrate around a point $x_0\inΩ$ as $ε\to 0$, moreover $x_0$ is a critical point of the Robin's function. Conversely, we show that for any nondegenerate critical point $x_0$ of the Robin's function, there exist solutions concentrating around $x_0$ as $ε$ goes to zero. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0412105 | |
| dc.identifier | http://arxiv.org/abs/math/0412105 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73491 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J65, 35J40, 58E05 | |
| dc.title | Single Blow up Solutions for a Slightly Subcritical Biharmonic Equation | |
| dc.type | text |