On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity

Detalhes bibliográficos
Autor(a) principal: Pimenta, Marcos T. O. [UNESP]
Data de Publicação: 2022
Outros Autores: Santos, Gelson Conceicao G. dos, Santos Junior, Joao R.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1017/prm.2022.86
http://hdl.handle.net/11449/245555
Resumo: In this work, we study a quasilinear elliptic problem involving the 1-Laplacian operator, with a discontinuous, superlinear and subcritical nonlinearity involving the Heaviside function H(middot - beta). Our approach is based on an analysis of the associated p-Laplacian problem, followed by a thorough analysis of the asymptotic behaviour or such solutions as p -> 1(+). We study also the asymptotic behaviour of the solutions, as beta -> 0(+) and we prove that it converges to a solution of the original problem, without the discontinuity in the nonlinearity.
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spelling On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity1-Laplacian operatorspace of functions of bounded variationdiscontinuous nonlinearitiesIn this work, we study a quasilinear elliptic problem involving the 1-Laplacian operator, with a discontinuous, superlinear and subcritical nonlinearity involving the Heaviside function H(middot - beta). Our approach is based on an analysis of the associated p-Laplacian problem, followed by a thorough analysis of the asymptotic behaviour or such solutions as p -> 1(+). We study also the asymptotic behaviour of the solutions, as beta -> 0(+) and we prove that it converges to a solution of the original problem, without the discontinuity in the nonlinearity.Funda��o de Amparo � Pesquisa do Estado de S�o Paulo (FAPESP)Conselho Nacional de Desenvolvimento Cient�fico e Tecnol�gico (CNPq)FAPDF, BrazilUniv Estadual Paulista Unesp, Dept Matemat & Computac, BR-19060900 Presidente Prudente, SP, BrazilUniv Fed Para, Fac Matemat, BR-66075110 Belem, PA, BrazilUniv Estadual Paulista Unesp, Dept Matemat & Computac, BR-19060900 Presidente Prudente, SP, BrazilFAPESP: 2021/04158-4FAPESP: 2021/10791-1CNPq: 303788/2018-6CNPq: 313766/2021-5Cambridge Univ PressUniversidade Estadual Paulista (UNESP)Univ Fed ParaPimenta, Marcos T. O. [UNESP]Santos, Gelson Conceicao G. dosSantos Junior, Joao R.2023-07-29T11:58:23Z2023-07-29T11:58:23Z2022-12-28info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article27http://dx.doi.org/10.1017/prm.2022.86Proceedings of the Royal Society of Edinburgh Section A-mathematics. Cambridge: Cambridge Univ Press, 27 p., 2022.0308-2105http://hdl.handle.net/11449/24555510.1017/prm.2022.86WOS:000904842100001Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengProceedings Of The Royal Society Of Edinburgh Section A-mathematicsinfo:eu-repo/semantics/openAccess2023-07-29T11:58:23Zoai:repositorio.unesp.br:11449/245555Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-07-29T11:58:23Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity
title On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity
spellingShingle On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity
Pimenta, Marcos T. O. [UNESP]
1-Laplacian operator
space of functions of bounded variation
discontinuous nonlinearities
title_short On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity
title_full On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity
title_fullStr On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity
title_full_unstemmed On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity
title_sort On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity
author Pimenta, Marcos T. O. [UNESP]
author_facet Pimenta, Marcos T. O. [UNESP]
Santos, Gelson Conceicao G. dos
Santos Junior, Joao R.
author_role author
author2 Santos, Gelson Conceicao G. dos
Santos Junior, Joao R.
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
Univ Fed Para
dc.contributor.author.fl_str_mv Pimenta, Marcos T. O. [UNESP]
Santos, Gelson Conceicao G. dos
Santos Junior, Joao R.
dc.subject.por.fl_str_mv 1-Laplacian operator
space of functions of bounded variation
discontinuous nonlinearities
topic 1-Laplacian operator
space of functions of bounded variation
discontinuous nonlinearities
description In this work, we study a quasilinear elliptic problem involving the 1-Laplacian operator, with a discontinuous, superlinear and subcritical nonlinearity involving the Heaviside function H(middot - beta). Our approach is based on an analysis of the associated p-Laplacian problem, followed by a thorough analysis of the asymptotic behaviour or such solutions as p -> 1(+). We study also the asymptotic behaviour of the solutions, as beta -> 0(+) and we prove that it converges to a solution of the original problem, without the discontinuity in the nonlinearity.
publishDate 2022
dc.date.none.fl_str_mv 2022-12-28
2023-07-29T11:58:23Z
2023-07-29T11:58:23Z
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/10.1017/prm.2022.86
Proceedings of the Royal Society of Edinburgh Section A-mathematics. Cambridge: Cambridge Univ Press, 27 p., 2022.
0308-2105
http://hdl.handle.net/11449/245555
10.1017/prm.2022.86
WOS:000904842100001
url http://dx.doi.org/10.1017/prm.2022.86
http://hdl.handle.net/11449/245555
identifier_str_mv Proceedings of the Royal Society of Edinburgh Section A-mathematics. Cambridge: Cambridge Univ Press, 27 p., 2022.
0308-2105
10.1017/prm.2022.86
WOS:000904842100001
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Proceedings Of The Royal Society Of Edinburgh Section A-mathematics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 27
dc.publisher.none.fl_str_mv Cambridge Univ Press
publisher.none.fl_str_mv Cambridge Univ Press
dc.source.none.fl_str_mv Web of Science
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_ 1797789915197472768

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