Introduction and results

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dc.contributor.authorByeon, Jaeyoungko
dc.contributor.authorTanaka, Kazunagako
dc.date.accessioned2014-12-16-
dc.date.available2014-12-16-
dc.date.created2014-06-30-
dc.date.created2014-06-30-
dc.date.created2014-06-30-
dc.date.issued2014-05-
dc.identifier.citationMEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, v.229, no.1076, pp.1 - 1-
dc.identifier.issn0065-9266-
dc.identifier.urihttp://hdl.handle.net/10203/192657-
dc.description.abstractWe study the following singularly perturbed problem -epsilon(2)Delta u + V(x)u = f(u) in R-N. Our main result is the existence of a family of solutions with peaks that cluster near a local maximum of V(x). A local variational and deformation argument in an infinite dimensional space is developed to establish the existence of such a family for a general class of nonlinearities f. Earlier works in this direction can be found in [KW, DLY, DY, NY] for f(xi) = xi(p) (1 < p < N+2/N-2 when N >= 3, 1 < p < infinity when N = 1, 2). These papers use the Lyapunov-Schmidt reduction method, where it is essential to have information about the null space of the linearization of a solution of the limit equation -Delta u + u = u(p). Such spectral information is difficult to get and can only be obtained for very special f's. Our new approach in this memoir does not require such a detailed knowledge of the spectrum and works for a much more general class of nonlinearities f.-
dc.languageEnglish-
dc.publisherAMER MATHEMATICAL SOC-
dc.titleIntroduction and results-
dc.typeArticle-
dc.identifier.wosid000348304500001-
dc.type.rimsART-
dc.citation.volume229-
dc.citation.issue1076-
dc.citation.beginningpage1-
dc.citation.endingpage1-
dc.citation.publicationnameMEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY-
dc.identifier.doi10.1090/memo/1076-
dc.embargo.liftdate9999-12-31-
dc.embargo.terms9999-12-31-
dc.contributor.localauthorByeon, Jaeyoung-
dc.contributor.nonIdAuthorTanaka, Kazunaga-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorNonlinear Schodinger equations-
dc.subject.keywordAuthorSingular perturbation-
dc.subject.keywordAuthorsemiclassical standing waves-
dc.subject.keywordAuthorlocal variational method-
dc.subject.keywordAuthorinteraction estimate-
dc.subject.keywordAuthortranslation flow-
dc.subject.keywordPlusNONLINEAR SCHRODINGER-EQUATIONS-
dc.subject.keywordPlusSTANDING WAVES-
dc.subject.keywordPlusSEMICLASSICAL STATES-
dc.subject.keywordPlusGENERAL NONLINEARITY-
dc.subject.keywordPlusBOUND-STATES-
dc.subject.keywordPlusMULTIPEAK SOLUTIONS-
dc.subject.keywordPlusELLIPTIC-EQUATIONS-
dc.subject.keywordPlusCRITICAL FREQUENCY-
dc.subject.keywordPlusUNBOUNDED-DOMAINS-
dc.subject.keywordPlusFIELD-EQUATIONS-
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