On the Henon equation with a Neumann boundary condition: Asymptotic profile of ground states

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dc.contributor.authorByeon, Jaeyoungko
dc.contributor.authorWang, Zhi-Qiangko
dc.date.accessioned2018-06-16T06:35:23Z-
dc.date.available2018-06-16T06:35:23Z-
dc.date.created2018-05-28-
dc.date.created2018-05-28-
dc.date.created2018-05-28-
dc.date.issued2018-06-
dc.identifier.citationJOURNAL OF FUNCTIONAL ANALYSIS, v.274, no.12, pp.3325 - 3376-
dc.identifier.issn0022-1236-
dc.identifier.urihttp://hdl.handle.net/10203/242402-
dc.description.abstractConsider the Henon equation with the homogeneous Neumann boundary condition -Delta u + u = |x|(alpha)u(p), u . 0 in Omega, partial derivative u/partial derivative v = 0 on partial derivative Omega, where Omega subset of B(0,1) subset of R-N, N >= 2 and partial derivative Omega boolean AND partial derivative B(0,1) # (sic). We are concerned on the asymptotic behavior of ground state solutions as the parameter alpha -> infinity. As alpha -> infinity, the non autonomous term Ixr is getting singular near vertical bar x vertical bar(alpha) = 1. The singular behavior of vertical bar x vertical bar(alpha) for large alpha > 0 forces the solution to blow up. Depending subtly on the (N - 1)-dimensional measure vertical bar partial derivative Omega boolean AND partial derivative B(0,1)vertical bar(N-1) and the nonlinear growth rate p, there are many different types of limiting profiles. To catch the asymptotic profiles, we take different types of renormalization depending on p and vertical bar partial derivative Omega boolean AND partial derivative B(0, 1)vertical bar(N-1). In particular, the critical exponent 2* = 2(N-1)/(N-2) for the Sobolev trace embedding plays a crucial role in the renormalization process. This is quite contrasted with the case of Dirichlet problems, where there is only one type of limiting profile for any p is an element of (1,2* -1) and a smooth domain Omega. (C) 2018 Elsevier Inc. All rights reserved.-
dc.languageEnglish-
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE-
dc.subjectNONLINEAR ELLIPTIC-EQUATIONS-
dc.subjectPOSITIVE SOLUTIONS-
dc.subjectCRITICAL GROWTH-
dc.subjectINEQUALITIES-
dc.subjectBEHAVIOR-
dc.subjectSYMMETRY-
dc.titleOn the Henon equation with a Neumann boundary condition: Asymptotic profile of ground states-
dc.typeArticle-
dc.identifier.wosid000431837000002-
dc.identifier.scopusid2-s2.0-85045217371-
dc.type.rimsART-
dc.citation.volume274-
dc.citation.issue12-
dc.citation.beginningpage3325-
dc.citation.endingpage3376-
dc.citation.publicationnameJOURNAL OF FUNCTIONAL ANALYSIS-
dc.identifier.doi10.1016/j.jfa.2018.03.015-
dc.contributor.localauthorByeon, Jaeyoung-
dc.contributor.nonIdAuthorWang, Zhi-Qiang-
dc.description.isOpenAccessN-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorLeast energy solutions-
dc.subject.keywordAuthorHenon equation-
dc.subject.keywordAuthorLimiting profile-
dc.subject.keywordAuthorNeumann boundary condition-
dc.subject.keywordPlusNONLINEAR ELLIPTIC-EQUATIONS-
dc.subject.keywordPlusPOSITIVE SOLUTIONS-
dc.subject.keywordPlusCRITICAL GROWTH-
dc.subject.keywordPlusINEQUALITIES-
dc.subject.keywordPlusBEHAVIOR-
dc.subject.keywordPlusSYMMETRY-
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