Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with d ≥ 3 equations
Autor(a) principal: | |
---|---|
Data de Publicação: | 2016 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.5/29106 |
Resumo: | In this work we consider the weakly coupled Schrödinger cubic system [vg. equation in attachment] where 1 ≤ N ≤ 3, λi, μi > 0 and bij = bji > 0 for i ≠ j. This system admits semitrivial solutions, that is solutions u = (u1, ..., ud) with null components. We provide optimal qualitative conditions on the parameters λi, μi and bij under which the ground state solutions have all components nontrivial, or, conversely, are semitrivial. This question had been clarified only in the d = 2 equations case. For d ≥ 3 equations, prior to the present paper, only very restrictive results were known, namely when the above system was a small perturbation of the super-symmetrical case λi ≡ λ and bij ≡ b. We treat the general case, uncovering in particular a much more complex and richer structure with respect to the d = 2 case |
id |
RCAP_a74f08241e62d577d662b839ef1bcacb |
---|---|
oai_identifier_str |
oai:www.repository.utl.pt:10400.5/29106 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with d ≥ 3 equationsSchrödinger Cubic System of Cooperative TypeGradient Elliptic SystemsGround StatesSemitrivial and Fully Nontrivial SolutionsIn this work we consider the weakly coupled Schrödinger cubic system [vg. equation in attachment] where 1 ≤ N ≤ 3, λi, μi > 0 and bij = bji > 0 for i ≠ j. This system admits semitrivial solutions, that is solutions u = (u1, ..., ud) with null components. We provide optimal qualitative conditions on the parameters λi, μi and bij under which the ground state solutions have all components nontrivial, or, conversely, are semitrivial. This question had been clarified only in the d = 2 equations case. For d ≥ 3 equations, prior to the present paper, only very restrictive results were known, namely when the above system was a small perturbation of the super-symmetrical case λi ≡ λ and bij ≡ b. We treat the general case, uncovering in particular a much more complex and richer structure with respect to the d = 2 caseElsevierRepositório da Universidade de LisboaCorreia, SimãoOliveira, FilipeTavares, Hugo2023-10-23T08:02:42Z20162016-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/29106engCorreia, Simão; Filipe Oliveira and Hugo Tavares .(2016). “Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with d ≥ 3 equations”. Journal of Functional Analysis, Volume 271, No. 8: pp. 2247-2273 . (Search PDF in 2023)0022-1236doi.org/10.1016/j.jfa.2016.06.017metadata only accessinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-10-29T01:30:45Zoai:www.repository.utl.pt:10400.5/29106Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:26:04.662718Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with d ≥ 3 equations |
title |
Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with d ≥ 3 equations |
spellingShingle |
Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with d ≥ 3 equations Correia, Simão Schrödinger Cubic System of Cooperative Type Gradient Elliptic Systems Ground States Semitrivial and Fully Nontrivial Solutions |
title_short |
Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with d ≥ 3 equations |
title_full |
Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with d ≥ 3 equations |
title_fullStr |
Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with d ≥ 3 equations |
title_full_unstemmed |
Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with d ≥ 3 equations |
title_sort |
Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with d ≥ 3 equations |
author |
Correia, Simão |
author_facet |
Correia, Simão Oliveira, Filipe Tavares, Hugo |
author_role |
author |
author2 |
Oliveira, Filipe Tavares, Hugo |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Repositório da Universidade de Lisboa |
dc.contributor.author.fl_str_mv |
Correia, Simão Oliveira, Filipe Tavares, Hugo |
dc.subject.por.fl_str_mv |
Schrödinger Cubic System of Cooperative Type Gradient Elliptic Systems Ground States Semitrivial and Fully Nontrivial Solutions |
topic |
Schrödinger Cubic System of Cooperative Type Gradient Elliptic Systems Ground States Semitrivial and Fully Nontrivial Solutions |
description |
In this work we consider the weakly coupled Schrödinger cubic system [vg. equation in attachment] where 1 ≤ N ≤ 3, λi, μi > 0 and bij = bji > 0 for i ≠ j. This system admits semitrivial solutions, that is solutions u = (u1, ..., ud) with null components. We provide optimal qualitative conditions on the parameters λi, μi and bij under which the ground state solutions have all components nontrivial, or, conversely, are semitrivial. This question had been clarified only in the d = 2 equations case. For d ≥ 3 equations, prior to the present paper, only very restrictive results were known, namely when the above system was a small perturbation of the super-symmetrical case λi ≡ λ and bij ≡ b. We treat the general case, uncovering in particular a much more complex and richer structure with respect to the d = 2 case |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016 2016-01-01T00:00:00Z 2023-10-23T08:02:42Z |
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://hdl.handle.net/10400.5/29106 |
url |
http://hdl.handle.net/10400.5/29106 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Correia, Simão; Filipe Oliveira and Hugo Tavares .(2016). “Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with d ≥ 3 equations”. Journal of Functional Analysis, Volume 271, No. 8: pp. 2247-2273 . (Search PDF in 2023) 0022-1236 doi.org/10.1016/j.jfa.2016.06.017 |
dc.rights.driver.fl_str_mv |
metadata only access info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
metadata only access |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
|
_version_ |
1799134142541070336 |