single blow-up solutions for a slightly subcritical biharmonic equation
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ID: 208507
2006
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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.
| Reference Key |
mehdi2006abstractsingle
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|---|---|
| Authors | ;Khalil El Mehdi |
| Journal | science and technology of advanced materials |
| Year | 2006 |
| DOI |
10.1155/AAA/2006/18387
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| URL | |
| Keywords |
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