Single blow‐up solutions for a slightly subcritical biharmonic equation

Khalil El Mehdi

Abstract and Applied Analysis, 2006, vol. 2006, issue 1

Abstract: We consider a biharmonic equation under the Navier boundary condition and with a nearly critical exponent (Pε): ∆2u = u9−ε, u > 0 in Ω and u = ∆u = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝ5, ε > 0. We study the asymptotic behavior of solutions of (Pε) which are minimizing for the Sobolev quotient as ε goes to zero. We show that such solutions concentrate around a point x0 ∈ Ω as ε → 0, moreover x0 is a critical point of the Robin′s function. Conversely, we show that for any nondegenerate critical point x0 of the Robin′s function, there exist solutions of (Pε) concentrating around x0 as ε → 0.

Date: 2006
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https://doi.org/10.1155/AAA/2006/18387

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2006:y:2006:i:1:n:018387

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