Abstract and Applied Analysis
Volume 2006 (2006), Article ID 18387, 20 pages
Single blow-up solutions for a slightly subcritical biharmonic equation
1Faculté des Sciences et Techniques, Université de Nouakchott, Nouakchott BP 5026, Mauritania
2The Abdus Salam ICTP, Trieste 34014, Italy
Received 29 October 2004; Accepted 20 January 2005
Copyright © 2006 Khalil El Mehdi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 .