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https://hdl.handle.net/1959.11/18795
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DC Field | Value | Language |
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dc.contributor.author | Yan, Shusen | en |
dc.contributor.author | Yang, Jianfu | en |
dc.contributor.author | Yu, Xiaohui | en |
dc.date.accessioned | 2016-04-01T14:19:00Z | - |
dc.date.issued | 2015 | - |
dc.identifier.citation | Journal of Functional Analysis, 269(1), p. 47-79 | en |
dc.identifier.issn | 1096-0783 | en |
dc.identifier.issn | 0022-1236 | en |
dc.identifier.uri | https://hdl.handle.net/1959.11/18795 | - |
dc.description.abstract | In this paper, we consider the following problem involving fractional Laplacian operator:(−Δ)αu=|u|2∗α-2-εu+λu in Ω, u = 0 on ∂Ω,(1) where Ω is a smooth bounded domain in RN, ε ∈[0, 2∗α−2), 0 < α < 1, 2∗α = 2N N-2α, and (−Δ)α is either the spectral fractional Laplacian or the restricted fractional Laplacian. We show for problem (1) with the spectral fractional Laplacian that for any sequence of solutions un of (1) corresponding to εn ∈ [0, 2∗α - 2), satisfying ǁunǁH ≤ C in the Sobolev space H defined in (1.2), un converges strongly in H provided that N > 6α and λ > 0. The same argument can also be used to obtain the same result for the restricted fractional Laplacian. An application of this compactness result is that problem (1) possesses infinitely many solutions under the same assumptions. | en |
dc.language | en | en |
dc.publisher | Elsevier Inc | en |
dc.relation.ispartof | Journal of Functional Analysis | en |
dc.title | Equations involving fractional Laplacian operator: Compactness and application | en |
dc.type | Journal Article | en |
dc.identifier.doi | 10.1016/j.jfa.2015.04.012 | en |
dcterms.accessRights | Green | en |
dc.subject.keywords | Partial Differential Equations | en |
local.contributor.firstname | Shusen | en |
local.contributor.firstname | Jianfu | en |
local.contributor.firstname | Xiaohui | en |
local.subject.for2008 | 010110 Partial Differential Equations | en |
local.subject.seo2008 | 970101 Expanding Knowledge in the Mathematical Sciences | en |
local.profile.school | School of Science and Technology | en |
local.profile.email | syan@une.edu.au | en |
local.profile.email | jfyang_2000@yahoo.com | en |
local.profile.email | yuxiao_211@163.com | en |
local.output.category | C1 | en |
local.record.place | au | en |
local.record.institution | University of New England | en |
local.identifier.epublicationsrecord | une-20160323-170954 | en |
local.publisher.place | United States of America | en |
local.format.startpage | 47 | en |
local.format.endpage | 79 | en |
local.url.open | https://arxiv.org/abs/1503.00788 | en |
local.peerreviewed | Yes | en |
local.identifier.volume | 269 | en |
local.identifier.issue | 1 | en |
local.title.subtitle | Compactness and application | en |
local.access.fulltext | Yes | en |
local.contributor.lastname | Yan | en |
local.contributor.lastname | Yang | en |
local.contributor.lastname | Yu | en |
dc.identifier.staff | une-id:syan | en |
local.profile.role | author | en |
local.profile.role | author | en |
local.profile.role | author | en |
local.identifier.unepublicationid | une:18996 | en |
dc.identifier.academiclevel | Academic | en |
local.title.maintitle | Equations involving fractional Laplacian operator | en |
local.output.categorydescription | C1 Refereed Article in a Scholarly Journal | en |
local.relation.grantdescription | ARC/DP130102773 | en |
local.search.author | Yan, Shusen | en |
local.search.author | Yang, Jianfu | en |
local.search.author | Yu, Xiaohui | en |
local.uneassociation | Unknown | en |
local.identifier.wosid | 000355239300002 | en |
local.year.published | 2015 | en |
local.subject.for2020 | 490410 Partial differential equations | en |
local.subject.seo2020 | 280118 Expanding knowledge in the mathematical sciences | en |
Appears in Collections: | Journal Article School of Science and Technology |
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