Large energy entire solutions for the Yamabe equation

Manuel Del Pino, Monica Musso, Frank Pacard, Angela Pistoia

Research output: Contribution to journalArticle

39 Citations (Scopus)

Abstract

We consider the Yamabe equation Δu+n(n-2)/4|u|4/n-2u=0 in R{double-struck}n, n≥3. Let k≥1 and ξj k=(e2jπi/k,0)εR{double-struck}n=C{double-struck}×R{double-struck}n-2. For all large k we find a solution of the form uk(x)=U(x)-σj=1 k;μk-n-2/2U×(μk -1(x-ξj))+o(1), where U(x)=(2/1+|x|2)n-2/2, μk=cn/k2 for n≥4, μk=c/k2(logk)2 for n=3 and o(1)→0 uniformly as k→+∞.

Original languageEnglish
Pages (from-to)2568-2597
Number of pages30
JournalJournal of Differential Equations
Volume251
Issue number9
DOIs
Publication statusPublished - 1 Nov 2011

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this