Single blow-up solutions for a slightly subcritical biharmonic equation

Khalil El Mehdi

Abstract and Applied Analysis, 2006, vol. 2006, 1-20

Abstract:

We consider a biharmonic equation under the Navier boundary condition and with a nearly critical exponent ( P ε ): ∆ 2 u = u 9 − ε , u > 0 in Ω and u = ∆ u = 0 on ∂ Ω , where Ω is a smooth bounded domain in ℝ 5 , ε > 0 . We study the asymptotic behavior of solutions of ( P ε ) which are minimizing for the Sobolev quotient as ε goes to zero. We show that such solutions concentrate around a point x 0 ∈ Ω as ε → 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 of ( P ε ) concentrating around x 0 as ε → 0 .

Date: 2006
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2006/018387.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2006/018387.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:018387

DOI: 10.1155/AAA/2006/18387

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().