Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2006 (2006), Article ID 18387, 20 pages.
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 (): , in and on , where is a smooth bounded domain in , . We study the asymptotic behavior of solutions of () which are minimizing for the Sobolev quotient as goes to zero. We show that such solutions concentrate around a point as , moreover is a critical point of the Robin's function. Conversely, we show that for any nondegenerate critical point of the Robin's function, there exist solutions of () concentrating around as .
Abstr. Appl. Anal., Volume 2006 (2006), Article ID 18387, 20 pages.
First available in Project Euclid: 30 January 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
El Mehdi, Khalil. Single blow-up solutions for a slightly subcritical biharmonic equation. Abstr. Appl. Anal. 2006 (2006), Article ID 18387, 20 pages. doi:10.1155/AAA/2006/18387. https://projecteuclid.org/euclid.aaa/1170202976