On an Elliptic Problem with Critical Nonlinearity in Expanding Annuli

✍ Scribed by Mohameden O. Ahmedou; Khalil O. El Mehdi

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 264 KB
• Volume: 163
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1998.3340

✦ Synopsis

This paper is concerned with an elliptic problem with homogeneous boundary conditions and critical nonlinearity (P = ): &2u=u p , u>0 on A = , u=0 on A = , where A = =[x # R n Â=<|x| <1Â=] are expanding annuli as = Ä 0, n 3 and p+1=2nÂ(n&2) is the critical Sobolev exponent. We compute the difference of topology induced by the critical points at infinity between the level sets of the functional corresponding to (P = ) for = small enough.

1999 Academic Press J(u)= 1 ( 0 |u| 2nÂ(n&2) ) (n&2)Ân