TITLE

SINGLE BLOW-UP SOLUTIONS FOR A SLIGHTLY SUBCRITICAL BIHARMONIC EQUATION

AUTHOR(S)
el Mehdi, Khalil
PUB. DATE
January 2006
SOURCE
Abstract & Applied Analysis;2006, p1
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We consider a biharmonic equation under the Navier boundary condition and with a nearly critical exponent (Pε): Δ²u = u9-ε, u > 0 in Ω and u = Δu = 0 on δΩ, 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 e 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.
ACCESSION #
24049414

 

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