Nodal solutions of an NLS equation concentrating on lower dimensional spheres
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1186/s13661-015-0411-8 http://hdl.handle.net/11449/168040 |
Resumo: | In this work we deal with the following nonlinear Schrödinger equation: {−<sup>ϵ2</sup>Δu+V(x)u=f(u)in <sup>RN</sup>u∈<sup>H1</sup>(<sup>RN</sup>),(Formula presented.) where N≥3, f is a subcritical power-type nonlinearity and V is a positive potential satisfying a local condition. We prove the existence and concentration of nodal solutions which concentrate around a k-dimensional sphere of R<sup>N</sup>, where (Formula presented.). The radius of such a sphere is related with the local minimum of a function which takes into account the potential V. Variational methods are used together with the penalization technique in order to overcome the lack of compactness. |
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Repositório Institucional da UNESP |
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Nodal solutions of an NLS equation concentrating on lower dimensional spheresconcentration on manifoldsnodal solutionsvariational methodsIn this work we deal with the following nonlinear Schrödinger equation: {−<sup>ϵ2</sup>Δu+V(x)u=f(u)in <sup>RN</sup>u∈<sup>H1</sup>(<sup>RN</sup>),(Formula presented.) where N≥3, f is a subcritical power-type nonlinearity and V is a positive potential satisfying a local condition. We prove the existence and concentration of nodal solutions which concentrate around a k-dimensional sphere of R<sup>N</sup>, where (Formula presented.). The radius of such a sphere is related with the local minimum of a function which takes into account the potential V. Variational methods are used together with the penalization technique in order to overcome the lack of compactness.Universidade Federal do ParáDepartamento de Matemática e Computação, Universidade Estadual Paulista - UnespDepartamento de Matemática e Computação, Universidade Estadual Paulista - UnespUniversidade Federal do Pará (UFPA)Universidade Estadual Paulista (Unesp)Figueiredo, Giovany MPimenta, Marcos T. O. [UNESP]2018-12-11T16:39:21Z2018-12-11T16:39:21Z2015-12-26info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://dx.doi.org/10.1186/s13661-015-0411-8Boundary Value Problems, v. 2015, n. 1, 2015.1687-27701687-2762http://hdl.handle.net/11449/16804010.1186/s13661-015-0411-82-s2.0-849422347332-s2.0-84942234733.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengBoundary Value Problems0,4900,490info:eu-repo/semantics/openAccess2023-12-20T06:25:08Zoai:repositorio.unesp.br:11449/168040Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T20:50:54.876641Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Nodal solutions of an NLS equation concentrating on lower dimensional spheres |
title |
Nodal solutions of an NLS equation concentrating on lower dimensional spheres |
spellingShingle |
Nodal solutions of an NLS equation concentrating on lower dimensional spheres Figueiredo, Giovany M concentration on manifolds nodal solutions variational methods |
title_short |
Nodal solutions of an NLS equation concentrating on lower dimensional spheres |
title_full |
Nodal solutions of an NLS equation concentrating on lower dimensional spheres |
title_fullStr |
Nodal solutions of an NLS equation concentrating on lower dimensional spheres |
title_full_unstemmed |
Nodal solutions of an NLS equation concentrating on lower dimensional spheres |
title_sort |
Nodal solutions of an NLS equation concentrating on lower dimensional spheres |
author |
Figueiredo, Giovany M |
author_facet |
Figueiredo, Giovany M Pimenta, Marcos T. O. [UNESP] |
author_role |
author |
author2 |
Pimenta, Marcos T. O. [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Federal do Pará (UFPA) Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Figueiredo, Giovany M Pimenta, Marcos T. O. [UNESP] |
dc.subject.por.fl_str_mv |
concentration on manifolds nodal solutions variational methods |
topic |
concentration on manifolds nodal solutions variational methods |
description |
In this work we deal with the following nonlinear Schrödinger equation: {−<sup>ϵ2</sup>Δu+V(x)u=f(u)in <sup>RN</sup>u∈<sup>H1</sup>(<sup>RN</sup>),(Formula presented.) where N≥3, f is a subcritical power-type nonlinearity and V is a positive potential satisfying a local condition. We prove the existence and concentration of nodal solutions which concentrate around a k-dimensional sphere of R<sup>N</sup>, where (Formula presented.). The radius of such a sphere is related with the local minimum of a function which takes into account the potential V. Variational methods are used together with the penalization technique in order to overcome the lack of compactness. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015-12-26 2018-12-11T16:39:21Z 2018-12-11T16:39:21Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1186/s13661-015-0411-8 Boundary Value Problems, v. 2015, n. 1, 2015. 1687-2770 1687-2762 http://hdl.handle.net/11449/168040 10.1186/s13661-015-0411-8 2-s2.0-84942234733 2-s2.0-84942234733.pdf |
url |
http://dx.doi.org/10.1186/s13661-015-0411-8 http://hdl.handle.net/11449/168040 |
identifier_str_mv |
Boundary Value Problems, v. 2015, n. 1, 2015. 1687-2770 1687-2762 10.1186/s13661-015-0411-8 2-s2.0-84942234733 2-s2.0-84942234733.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Boundary Value Problems 0,490 0,490 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129257379987456 |