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 language | English |
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Pages (from-to) | 2568-2597 |
Number of pages | 30 |
Journal | Journal of Differential Equations |
Volume | 251 |
Issue number | 9 |
DOIs | |
Publication status | Published - 1 Nov 2011 |
Funding
The first author is partially supported by Fondecyt Grant 1070389, Fondo Basal CMM and CAPDE-Anillo ACT-125. The second author is partially supported by Fondecyt Grant 1080099 and CAPDE-Anillo ACT-125. The third author is partially supported by the ANR-08-BLANC-0335-01 grant. The last author is supported by the Mi.U.R. National Project Metodi variazionali e topologici nello studio di fenomeni non lineari.
ASJC Scopus subject areas
- Analysis
- Applied Mathematics