Symmetry and symmetry breaking for Hénon-type problems involving the 1-Laplacian operator

Detalhes bibliográficos
Autor(a) principal: Pimenta, Marcos T. O. [UNESP]
Data de Publicação: 2022
Outros Autores: Gonzaga, Anderson dos Santos [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1142/S0219199722500213
http://hdl.handle.net/11449/241079
Resumo: In this work, we study a class of Hénon-type equations which involve the 1-Laplacian operator in the unit ball. Under mild assumptions on the nonlinearity, the existence of radial solutions is proved and, for a parameter in a certain range, the existence of symmetry breaking is proved, through the presence of non-radial solutions. The approach is based on an approximation scheme, where a thorough analysis of the solutions of the associated p-Laplacian problems is necessary.
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spelling Symmetry and symmetry breaking for Hénon-type problems involving the 1-Laplacian operator1-Laplacian operatorHénon-type equationspace of functions of bounded variationsymmetry breakingIn this work, we study a class of Hénon-type equations which involve the 1-Laplacian operator in the unit ball. Under mild assumptions on the nonlinearity, the existence of radial solutions is proved and, for a parameter in a certain range, the existence of symmetry breaking is proved, through the presence of non-radial solutions. The approach is based on an approximation scheme, where a thorough analysis of the solutions of the associated p-Laplacian problems is necessary.Departamento de Matemática e Computação Universidade Estadual Paulista - Unesp, CEP: 19060-900 Presidente Prudente, SPDepartamento de Matemática Instituto de Biociências Letras e Ciências Exatas - Ibilce/Unesp, CEP: 15054-000 São José do Rio Preto, SPDepartamento de Matemática e Computação Universidade Estadual Paulista - Unesp, CEP: 19060-900 Presidente Prudente, SPDepartamento de Matemática Instituto de Biociências Letras e Ciências Exatas - Ibilce/Unesp, CEP: 15054-000 São José do Rio Preto, SPUniversidade Estadual Paulista (UNESP)Pimenta, Marcos T. O. [UNESP]Gonzaga, Anderson dos Santos [UNESP]2023-03-01T20:46:13Z2023-03-01T20:46:13Z2022-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1142/S0219199722500213Communications in Contemporary Mathematics.0219-1997http://hdl.handle.net/11449/24107910.1142/S02191997225002132-s2.0-85131072961Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengCommunications in Contemporary Mathematicsinfo:eu-repo/semantics/openAccess2023-03-01T20:46:13Zoai:repositorio.unesp.br:11449/241079Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-03-01T20:46:13Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Symmetry and symmetry breaking for Hénon-type problems involving the 1-Laplacian operator
title Symmetry and symmetry breaking for Hénon-type problems involving the 1-Laplacian operator
spellingShingle Symmetry and symmetry breaking for Hénon-type problems involving the 1-Laplacian operator
Pimenta, Marcos T. O. [UNESP]
1-Laplacian operator
Hénon-type equation
space of functions of bounded variation
symmetry breaking
title_short Symmetry and symmetry breaking for Hénon-type problems involving the 1-Laplacian operator
title_full Symmetry and symmetry breaking for Hénon-type problems involving the 1-Laplacian operator
title_fullStr Symmetry and symmetry breaking for Hénon-type problems involving the 1-Laplacian operator
title_full_unstemmed Symmetry and symmetry breaking for Hénon-type problems involving the 1-Laplacian operator
title_sort Symmetry and symmetry breaking for Hénon-type problems involving the 1-Laplacian operator
author Pimenta, Marcos T. O. [UNESP]
author_facet Pimenta, Marcos T. O. [UNESP]
Gonzaga, Anderson dos Santos [UNESP]
author_role author
author2 Gonzaga, Anderson dos Santos [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Pimenta, Marcos T. O. [UNESP]
Gonzaga, Anderson dos Santos [UNESP]
dc.subject.por.fl_str_mv 1-Laplacian operator
Hénon-type equation
space of functions of bounded variation
symmetry breaking
topic 1-Laplacian operator
Hénon-type equation
space of functions of bounded variation
symmetry breaking
description In this work, we study a class of Hénon-type equations which involve the 1-Laplacian operator in the unit ball. Under mild assumptions on the nonlinearity, the existence of radial solutions is proved and, for a parameter in a certain range, the existence of symmetry breaking is proved, through the presence of non-radial solutions. The approach is based on an approximation scheme, where a thorough analysis of the solutions of the associated p-Laplacian problems is necessary.
publishDate 2022
dc.date.none.fl_str_mv 2022-01-01
2023-03-01T20:46:13Z
2023-03-01T20:46:13Z
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/10.1142/S0219199722500213
Communications in Contemporary Mathematics.
0219-1997
http://hdl.handle.net/11449/241079
10.1142/S0219199722500213
2-s2.0-85131072961
url http://dx.doi.org/10.1142/S0219199722500213
http://hdl.handle.net/11449/241079
identifier_str_mv Communications in Contemporary Mathematics.
0219-1997
10.1142/S0219199722500213
2-s2.0-85131072961
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Communications in Contemporary Mathematics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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_ 1797790071522328576

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