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https://hdl.handle.net/1959.11/7480
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DC Field | Value | Language |
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dc.contributor.author | Wei, Juncheng | en |
dc.contributor.author | Yan, Shusen | en |
dc.date.accessioned | 2011-05-19T10:58:00Z | - |
dc.date.issued | 2010 | - |
dc.identifier.citation | Journal of Functional Analysis, 258(9), p. 3048-3081 | en |
dc.identifier.issn | 1096-0783 | en |
dc.identifier.issn | 0022-1236 | en |
dc.identifier.uri | https://hdl.handle.net/1959.11/7480 | - |
dc.description.abstract | In this paper, we consider the simplest case, i.e., K is rotationally symmetric, K = K(r), r = |y|. It follows from the Pohozaev identity (1.2) that (1.6) has no solution if K'(r) has fixed sign. Thus we assume that K is positive and not monotone. On the other hand, Bianchi [5] showed that any solution of (1.6) is radially symmetric if there is an rₒ > 0, such that K(r) is non-increasing in (0, rₒ], and non-decreasing in [rₒ,+∞). Moreover, in [6], it was proved that (1.6) has no solutions for some function K(r), which is non-increasing in (0, 1], and nondecreasing in [1,+∞). Therefore, we see that to obtain a solution for (1.6), it is natural to assume that K(r) has a local maximum at rₒ > 0. The purpose of this paper is to answer the following two questions: Q1. Does the existence of a local maximum of K guarantee the existence of a solution to (1.6)? Q2. Are there non-radially symmetric solutions to (1.6)? | en |
dc.language | en | en |
dc.publisher | Elsevier Inc | en |
dc.relation.ispartof | Journal of Functional Analysis | en |
dc.title | Infinitely many solutions for the prescribed scalar curvature problem on Sᴺ | en |
dc.type | Journal Article | en |
dc.identifier.doi | 10.1016/j.jfa.2009.12.008 | en |
dc.subject.keywords | Partial Differential Equations | en |
local.contributor.firstname | Juncheng | en |
local.contributor.firstname | Shusen | en |
local.subject.for2008 | 010110 Partial Differential Equations | en |
local.subject.seo2008 | 970101 Expanding Knowledge in the Mathematical Sciences | en |
local.profile.school | Maths | en |
local.profile.school | School of Science and Technology | en |
local.profile.email | wei@math.cuhk.edu.hk | en |
local.profile.email | syan@une.edu.au | en |
local.output.category | C1 | en |
local.record.place | au | en |
local.record.institution | University of New England | en |
local.identifier.epublicationsrecord | une-20110325-110527 | en |
local.publisher.place | United States of America | en |
local.format.startpage | 3048 | en |
local.format.endpage | 3081 | en |
local.peerreviewed | Yes | en |
local.identifier.volume | 258 | en |
local.identifier.issue | 9 | en |
local.contributor.lastname | Wei | en |
local.contributor.lastname | Yan | en |
dc.identifier.staff | une-id:syan | en |
local.profile.role | author | en |
local.profile.role | author | en |
local.identifier.unepublicationid | une:7648 | en |
dc.identifier.academiclevel | Academic | en |
dc.identifier.academiclevel | Academic | en |
local.title.maintitle | Infinitely many solutions for the prescribed scalar curvature problem on Sᴺ | en |
local.output.categorydescription | C1 Refereed Article in a Scholarly Journal | en |
local.search.author | Wei, Juncheng | en |
local.search.author | Yan, Shusen | en |
local.uneassociation | Unknown | en |
local.identifier.wosid | 000275303900008 | en |
local.year.published | 2010 | en |
Appears in Collections: | Journal Article |
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