Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da UFPB |
Texto Completo: | https://repositorio.ufpb.br/jspui/handle/123456789/15373 |
Resumo: | In this work we study the asymptotic behavior to positive solutions of the following coupled elliptic system of nonlinear Schrödinger equations ∆gui − 2 X j=1 Aij(x)uj + n(n−2) 4 |U| 4 n−2ui = 0 which are defined in the punctured unit ball B1(0)\{0} for n ≥ 3. Here g is a Riemannian metric on the unit ball and the potential A is assumed a C1 map such that Aij(x) is a symmetrical matrix for each x in B1(0). From the viewpoint of conformal geometry, this systems are pure extensions of Yamabe-type equations. We will approach the problem assuming first that g is the euclidian metric and the potential A vanishes. In this case we are able to prove that the solutions of our problem are asymptotics to what we call Fowler-type solutions. In the general case we will prove the same result by putting some restrictions on the potential and assuming that the dimension is less or equal to five. |
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Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponentSoluções do tipo FowlerComportamento assintóticoSistemas do tipo YamabeFowler-type solutionsAsymptotic behaviorYamabe-type systemCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAIn this work we study the asymptotic behavior to positive solutions of the following coupled elliptic system of nonlinear Schrödinger equations ∆gui − 2 X j=1 Aij(x)uj + n(n−2) 4 |U| 4 n−2ui = 0 which are defined in the punctured unit ball B1(0)\{0} for n ≥ 3. Here g is a Riemannian metric on the unit ball and the potential A is assumed a C1 map such that Aij(x) is a symmetrical matrix for each x in B1(0). From the viewpoint of conformal geometry, this systems are pure extensions of Yamabe-type equations. We will approach the problem assuming first that g is the euclidian metric and the potential A vanishes. In this case we are able to prove that the solutions of our problem are asymptotics to what we call Fowler-type solutions. In the general case we will prove the same result by putting some restrictions on the potential and assuming that the dimension is less or equal to five.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESNeste trabalho estudaremos o comportamento assintótico de soluções positivas do seguinte sistema elípticos acoplado de equações de Schrödinger não lineares ∆gui − 2 X j=1 Aij(x)uj + n(n−2) 4 |U| 4 n−2ui = 0 definido em B1(0)\{0}para n ≥ 3, onde g é uma métrica Riemanniana na bola unitária e o potential A é um mapa de classe C1 tal que Aij(x) é uma matriz simétrica para cada x pertencente a B1(0). Do ponto de vista da geometria conforme, o sistema acima é uma extensão natural de equações do tipo Yamabe. Abordaremos o problema assumindo primeiramente que g é a métrica euclidiana e que o potencial A é identicamente nulo. Nesse caso iremos provar que as soluções do nosso problema são assintóticas ao que chamaremos de soluções do tipo Fowler. No caso geral, iremos demonstrar que o mesmo resultado inserindo algumas restrições sobre o potencial e assumindo que a dimensão é menor ou igual a cinco.Universidade Federal da ParaíbaBrasilMatemáticaPrograma de Pós-Graduação em MatemáticaUFPBÓ, João Marcos Bezerra dohttp://lattes.cnpq.br/6069135199129029Marques, Fernando Codá dos Santos CavalcantiCaju, Rayssa Helena Aires de Lima2019-08-26T16:55:36Z2019-08-262019-08-26T16:55:36Z2018-02-23info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesishttps://repositorio.ufpb.br/jspui/handle/123456789/15373porAttribution-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nd/3.0/br/info:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da UFPBinstname:Universidade Federal da Paraíba (UFPB)instacron:UFPB2019-08-27T06:06:53Zoai:repositorio.ufpb.br:123456789/15373Biblioteca Digital de Teses e Dissertaçõeshttps://repositorio.ufpb.br/PUBhttp://tede.biblioteca.ufpb.br:8080/oai/requestdiretoria@ufpb.br|| diretoria@ufpb.bropendoar:2019-08-27T06:06:53Biblioteca Digital de Teses e Dissertações da UFPB - Universidade Federal da Paraíba (UFPB)false |
dc.title.none.fl_str_mv |
Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent |
title |
Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent |
spellingShingle |
Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent Caju, Rayssa Helena Aires de Lima Soluções do tipo Fowler Comportamento assintótico Sistemas do tipo Yamabe Fowler-type solutions Asymptotic behavior Yamabe-type system CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent |
title_full |
Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent |
title_fullStr |
Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent |
title_full_unstemmed |
Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent |
title_sort |
Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent |
author |
Caju, Rayssa Helena Aires de Lima |
author_facet |
Caju, Rayssa Helena Aires de Lima |
author_role |
author |
dc.contributor.none.fl_str_mv |
Ó, João Marcos Bezerra do http://lattes.cnpq.br/6069135199129029 Marques, Fernando Codá dos Santos Cavalcanti |
dc.contributor.author.fl_str_mv |
Caju, Rayssa Helena Aires de Lima |
dc.subject.por.fl_str_mv |
Soluções do tipo Fowler Comportamento assintótico Sistemas do tipo Yamabe Fowler-type solutions Asymptotic behavior Yamabe-type system CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
topic |
Soluções do tipo Fowler Comportamento assintótico Sistemas do tipo Yamabe Fowler-type solutions Asymptotic behavior Yamabe-type system CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
In this work we study the asymptotic behavior to positive solutions of the following coupled elliptic system of nonlinear Schrödinger equations ∆gui − 2 X j=1 Aij(x)uj + n(n−2) 4 |U| 4 n−2ui = 0 which are defined in the punctured unit ball B1(0)\{0} for n ≥ 3. Here g is a Riemannian metric on the unit ball and the potential A is assumed a C1 map such that Aij(x) is a symmetrical matrix for each x in B1(0). From the viewpoint of conformal geometry, this systems are pure extensions of Yamabe-type equations. We will approach the problem assuming first that g is the euclidian metric and the potential A vanishes. In this case we are able to prove that the solutions of our problem are asymptotics to what we call Fowler-type solutions. In the general case we will prove the same result by putting some restrictions on the potential and assuming that the dimension is less or equal to five. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-02-23 2019-08-26T16:55:36Z 2019-08-26 2019-08-26T16:55:36Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufpb.br/jspui/handle/123456789/15373 |
url |
https://repositorio.ufpb.br/jspui/handle/123456789/15373 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.rights.driver.fl_str_mv |
Attribution-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nd/3.0/br/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Attribution-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal da Paraíba Brasil Matemática Programa de Pós-Graduação em Matemática UFPB |
publisher.none.fl_str_mv |
Universidade Federal da Paraíba Brasil Matemática Programa de Pós-Graduação em Matemática UFPB |
dc.source.none.fl_str_mv |
reponame:Biblioteca Digital de Teses e Dissertações da UFPB instname:Universidade Federal da Paraíba (UFPB) instacron:UFPB |
instname_str |
Universidade Federal da Paraíba (UFPB) |
instacron_str |
UFPB |
institution |
UFPB |
reponame_str |
Biblioteca Digital de Teses e Dissertações da UFPB |
collection |
Biblioteca Digital de Teses e Dissertações da UFPB |
repository.name.fl_str_mv |
Biblioteca Digital de Teses e Dissertações da UFPB - Universidade Federal da Paraíba (UFPB) |
repository.mail.fl_str_mv |
diretoria@ufpb.br|| diretoria@ufpb.br |
_version_ |
1801842953195356160 |