Existence of solutions to a 1-Laplacian problem with a concave-convex nonlinearity
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.jmaa.2023.127149 http://hdl.handle.net/11449/246944 |
Resumo: | In this paper, we analyze a “concave-convex” type problem involving the 1-Laplacian operator in a general Lipschitz–continuous domain and prove the existence of two positive solutions. Owing to 1-Laplacian is 0-homogeneous, the “concave” term must be singular. Hence, we should deal with an energy functional having two non–differentiable terms: the total variation and that one coming from the singular term. Due to these difficulties, we do not get solutions as critical points of the energy functional defined in the BV(Ω) space. Instead, we study problems involving the p-Laplacian operator and let p go to 1. |
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Existence of solutions to a 1-Laplacian problem with a concave-convex nonlinearity1-Laplacian operatorConcave-convex nonlinearitiesSingular termIn this paper, we analyze a “concave-convex” type problem involving the 1-Laplacian operator in a general Lipschitz–continuous domain and prove the existence of two positive solutions. Owing to 1-Laplacian is 0-homogeneous, the “concave” term must be singular. Hence, we should deal with an energy functional having two non–differentiable terms: the total variation and that one coming from the singular term. Due to these difficulties, we do not get solutions as critical points of the energy functional defined in the BV(Ω) space. Instead, we study problems involving the p-Laplacian operator and let p go to 1.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselleria de Innovación, Universidades, Ciencia y Sociedad Digital, Generalitat ValencianaDepartamento de Matemática e Computação Universidade Estadual Paulista - Unesp, SPDepartament d'Anàlisi Matemàtica Universitat de València, BurjassotDepartamento de Matemática e Computação Universidade Estadual Paulista - Unesp, SPFAPESP: 2017/06119-0FAPESP: 2019/13503-7FAPESP: 2021/04158-4CNPq: 304765/2021-0Conselleria de Innovación, Universidades, Ciencia y Sociedad Digital, Generalitat Valenciana: AICO/2021/223Universidade Estadual Paulista (UNESP)Universitat de ValènciaChata, Juan Carlos Ortiz [UNESP]Pimenta, Marcos T.O. [UNESP]de León, Sergio Segura2023-07-29T12:54:52Z2023-07-29T12:54:52Z2023-09-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.jmaa.2023.127149Journal of Mathematical Analysis and Applications, v. 525, n. 2, 2023.1096-08130022-247Xhttp://hdl.handle.net/11449/24694410.1016/j.jmaa.2023.1271492-s2.0-85149458264Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Mathematical Analysis and Applicationsinfo:eu-repo/semantics/openAccess2023-07-29T12:54:52Zoai:repositorio.unesp.br:11449/246944Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:48:57.507459Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Existence of solutions to a 1-Laplacian problem with a concave-convex nonlinearity |
title |
Existence of solutions to a 1-Laplacian problem with a concave-convex nonlinearity |
spellingShingle |
Existence of solutions to a 1-Laplacian problem with a concave-convex nonlinearity Chata, Juan Carlos Ortiz [UNESP] 1-Laplacian operator Concave-convex nonlinearities Singular term |
title_short |
Existence of solutions to a 1-Laplacian problem with a concave-convex nonlinearity |
title_full |
Existence of solutions to a 1-Laplacian problem with a concave-convex nonlinearity |
title_fullStr |
Existence of solutions to a 1-Laplacian problem with a concave-convex nonlinearity |
title_full_unstemmed |
Existence of solutions to a 1-Laplacian problem with a concave-convex nonlinearity |
title_sort |
Existence of solutions to a 1-Laplacian problem with a concave-convex nonlinearity |
author |
Chata, Juan Carlos Ortiz [UNESP] |
author_facet |
Chata, Juan Carlos Ortiz [UNESP] Pimenta, Marcos T.O. [UNESP] de León, Sergio Segura |
author_role |
author |
author2 |
Pimenta, Marcos T.O. [UNESP] de León, Sergio Segura |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (UNESP) Universitat de València |
dc.contributor.author.fl_str_mv |
Chata, Juan Carlos Ortiz [UNESP] Pimenta, Marcos T.O. [UNESP] de León, Sergio Segura |
dc.subject.por.fl_str_mv |
1-Laplacian operator Concave-convex nonlinearities Singular term |
topic |
1-Laplacian operator Concave-convex nonlinearities Singular term |
description |
In this paper, we analyze a “concave-convex” type problem involving the 1-Laplacian operator in a general Lipschitz–continuous domain and prove the existence of two positive solutions. Owing to 1-Laplacian is 0-homogeneous, the “concave” term must be singular. Hence, we should deal with an energy functional having two non–differentiable terms: the total variation and that one coming from the singular term. Due to these difficulties, we do not get solutions as critical points of the energy functional defined in the BV(Ω) space. Instead, we study problems involving the p-Laplacian operator and let p go to 1. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-07-29T12:54:52Z 2023-07-29T12:54:52Z 2023-09-15 |
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/10.1016/j.jmaa.2023.127149 Journal of Mathematical Analysis and Applications, v. 525, n. 2, 2023. 1096-0813 0022-247X http://hdl.handle.net/11449/246944 10.1016/j.jmaa.2023.127149 2-s2.0-85149458264 |
url |
http://dx.doi.org/10.1016/j.jmaa.2023.127149 http://hdl.handle.net/11449/246944 |
identifier_str_mv |
Journal of Mathematical Analysis and Applications, v. 525, n. 2, 2023. 1096-0813 0022-247X 10.1016/j.jmaa.2023.127149 2-s2.0-85149458264 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal of Mathematical Analysis and Applications |
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_ |
1808129122663137280 |