DC Field | Value | Language |
---|---|---|
dc.contributor.author | Byeon, Jaeyoung | ko |
dc.contributor.author | Tanaka, Kazunaga | ko |
dc.date.accessioned | 2014-12-16 | - |
dc.date.available | 2014-12-16 | - |
dc.date.created | 2014-06-30 | - |
dc.date.created | 2014-06-30 | - |
dc.date.created | 2014-06-30 | - |
dc.date.issued | 2014-05 | - |
dc.identifier.citation | MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, v.229, no.1076, pp.1 - 1 | - |
dc.identifier.issn | 0065-9266 | - |
dc.identifier.uri | http://hdl.handle.net/10203/192657 | - |
dc.description.abstract | We 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.language | English | - |
dc.publisher | AMER MATHEMATICAL SOC | - |
dc.title | Introduction and results | - |
dc.type | Article | - |
dc.identifier.wosid | 000348304500001 | - |
dc.type.rims | ART | - |
dc.citation.volume | 229 | - |
dc.citation.issue | 1076 | - |
dc.citation.beginningpage | 1 | - |
dc.citation.endingpage | 1 | - |
dc.citation.publicationname | MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY | - |
dc.identifier.doi | 10.1090/memo/1076 | - |
dc.embargo.liftdate | 9999-12-31 | - |
dc.embargo.terms | 9999-12-31 | - |
dc.contributor.localauthor | Byeon, Jaeyoung | - |
dc.contributor.nonIdAuthor | Tanaka, Kazunaga | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | Nonlinear Schodinger equations | - |
dc.subject.keywordAuthor | Singular perturbation | - |
dc.subject.keywordAuthor | semiclassical standing waves | - |
dc.subject.keywordAuthor | local variational method | - |
dc.subject.keywordAuthor | interaction estimate | - |
dc.subject.keywordAuthor | translation flow | - |
dc.subject.keywordPlus | NONLINEAR SCHRODINGER-EQUATIONS | - |
dc.subject.keywordPlus | STANDING WAVES | - |
dc.subject.keywordPlus | SEMICLASSICAL STATES | - |
dc.subject.keywordPlus | GENERAL NONLINEARITY | - |
dc.subject.keywordPlus | BOUND-STATES | - |
dc.subject.keywordPlus | MULTIPEAK SOLUTIONS | - |
dc.subject.keywordPlus | ELLIPTIC-EQUATIONS | - |
dc.subject.keywordPlus | CRITICAL FREQUENCY | - |
dc.subject.keywordPlus | UNBOUNDED-DOMAINS | - |
dc.subject.keywordPlus | FIELD-EQUATIONS | - |
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