Single Blow up Solutions for a Slightly Subcritical Biharmonic Equation

dc.creatorMehdi, Khalil El
dc.date2004-12-06
dc.date.accessioned2026-07-07T05:14:58Z
dc.date.available2026-07-07T05:14:58Z
dc.descriptionIn 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.description19 pages
dc.identifierhttps://arxiv.org/abs/math/0412105
dc.identifierhttp://arxiv.org/abs/math/0412105
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73491
dc.subjectAnalysis of PDEs
dc.subject35J65, 35J40, 58E05
dc.titleSingle Blow up Solutions for a Slightly Subcritical Biharmonic Equation
dc.typetext

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