Existence of solutions to a 1-Laplacian problem with a concave-convex nonlinearity

Detalhes bibliográficos
Autor(a) principal: Chata, Juan Carlos Ortiz [UNESP]
Data de Publicação: 2023
Outros Autores: Pimenta, Marcos T.O. [UNESP], de León, Sergio Segura
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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spelling 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)
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