A Morse lemma at infinity for Yamabe type problems on domains

✍ Scribed by Mohamed Ben Ayed; Hichem Chtioui; Mokhless Hammami

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 272 KB
• Volume: 20
• Category: Article
• ISSN: 0294-1449
• DOI: 10.1016/s0294-1449(02)00020-3

✦ Synopsis

In this paper we consider the following nonlinear elliptic problem (P):u = u p , u > 0 in , u = 0 on ∂ , where is a bounded and smooth domain in R n , n 4, p + 1 = 2n/(n -2) is the critical Sobolev exponent. We prove a version of Morse lemmas at infinity for this problem. As application of these lemmas we will give a characterization of the critical points at infinity of the functional corresponding to (P).