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Large energy entire solutions for the Yamabe equation

descriptionPublicationkeyboard_double_arrow_right Article 01 Nov 2011 English Publisher:Elsevier BVJournal:Journal of Differential Equations, volume 251, pages 2,568-2,597 (issn: 0022-0396, Copyright policy )
Authors: Frank Pacard; Frank Pacard; Monica Musso; Manuel del Pino; Angela Pistoia;

doi: 10.1016/j.jde.2011.03.008

handle: 10533/130158 , 10533/130157 , 11573/380826

Large energy entire solutions for the Yamabe equation

Abstract

AbstractWe consider the Yamabe equation Δu+n(n−2)4|u|4n−2u=0 in Rn, n⩾3. Let k⩾1 and ξjk=(e2jπik,0)∈Rn=C×Rn−2. For all large k we find a solution of the form uk(x)=U(x)−∑j=1kμk−n−22U×(μk−1(x−ξj))+o(1), where U(x)=(21+|x|2)n−22, μk=cnk2 for n⩾4, μk=ck2(logk)2 for n=3 and o(1)→0 uniformly as k→+∞.

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Keywords

BLOW-UP, GLOBAL WELL-POSEDNESS, ELLIPTIC-EQUATIONS, CRITICAL SOBOLEV GROWTH, SCATTERING, [MATH]Mathematics [math], 530, Analysis, 510

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
79
Top 10%
Top 10%
Top 10%
Green
hybrid