Single blow-up solutions for a slightly subcritical biharmonic equation
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 quotien...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA/2006/18387 |
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| _version_ | 1849435072347766784 |
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| author | Khalil El Mehdi |
| author_facet | Khalil El Mehdi |
| author_sort | Khalil El Mehdi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e4f704ef74f24894a4d6491c09d4e017 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e4f704ef74f24894a4d6491c09d4e0172025-08-20T03:26:25ZengWileyAbstract and Applied Analysis1085-33751687-04092006-01-01200610.1155/AAA/2006/1838718387Single blow-up solutions for a slightly subcritical biharmonic equationKhalil El Mehdi0Faculté des Sciences et Techniques, Université de Nouakchott, Nouakchott BP 5026, MauritaniaWe 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.http://dx.doi.org/10.1155/AAA/2006/18387 |
| spellingShingle | Khalil El Mehdi Single blow-up solutions for a slightly subcritical biharmonic equation Abstract and Applied Analysis |
| title | Single blow-up solutions for a slightly subcritical biharmonic equation |
| title_full | Single blow-up solutions for a slightly subcritical biharmonic equation |
| title_fullStr | Single blow-up solutions for a slightly subcritical biharmonic equation |
| title_full_unstemmed | Single blow-up solutions for a slightly subcritical biharmonic equation |
| title_short | Single blow-up solutions for a slightly subcritical biharmonic equation |
| title_sort | single blow up solutions for a slightly subcritical biharmonic equation |
| url | http://dx.doi.org/10.1155/AAA/2006/18387 |
| work_keys_str_mv | AT khalilelmehdi singleblowupsolutionsforaslightlysubcriticalbiharmonicequation |