2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73491In 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.19 pagesAnalysis of PDEs35J65, 35J40, 58E05text