A Berestycki-Lions' type result to a quasilinear elliptic problem involving the 1-Laplacian operator
Autor(a) principal: | |
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Data de Publicação: | 2021 |
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.2021.125074 http://hdl.handle.net/11449/205911 |
Resumo: | In this work we study a quasilinear elliptic problem involving the 1-Laplacian operator in RN, whose nonlinearity satisfy conditions similar to those ones of the classical work of Berestycki and Lions. Several difficulties are faced when trying to generalize the arguments of the semilinear case, to this quasilinear problem. The main existence theorem is proved through a new version of the well known Mountain Pass Theorem to locally Lipschitz functionals, where it is considered the Cerami compactness condition rather than the Palais-Smale one. It is also proved that all bounded variation solutions which are regular enough, satisfy a Pohozaev type identity. |
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A Berestycki-Lions' type result to a quasilinear elliptic problem involving the 1-Laplacian operator1-Laplacian operatorBounded variation functionsPohozaev identityIn this work we study a quasilinear elliptic problem involving the 1-Laplacian operator in RN, whose nonlinearity satisfy conditions similar to those ones of the classical work of Berestycki and Lions. Several difficulties are faced when trying to generalize the arguments of the semilinear case, to this quasilinear problem. The main existence theorem is proved through a new version of the well known Mountain Pass Theorem to locally Lipschitz functionals, where it is considered the Cerami compactness condition rather than the Palais-Smale one. It is also proved that all bounded variation solutions which are regular enough, satisfy a Pohozaev type identity.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Departamento de Matemática Universidade Estadual Paulista - UnespDepartamento de Matemática e Computação Universidade Estadual Paulista - UnespDepartamento de Matemática Universidade Estadual Paulista - UnespDepartamento de Matemática e Computação Universidade Estadual Paulista - UnespFAPESP: 2017/06119-0FAPESP: 2019/13503-7FAPESP: 2019/14330-9CNPq: 303788/2018-6Universidade Estadual Paulista (Unesp)Ortiz Chata, Juan C. [UNESP]Pimenta, Marcos T.O. [UNESP]2021-06-25T10:23:20Z2021-06-25T10:23:20Z2021-08-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.jmaa.2021.125074Journal of Mathematical Analysis and Applications, v. 500, n. 1, 2021.1096-08130022-247Xhttp://hdl.handle.net/11449/20591110.1016/j.jmaa.2021.1250742-s2.0-85101176994Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Mathematical Analysis and Applicationsinfo:eu-repo/semantics/openAccess2021-10-22T17:02:16Zoai:repositorio.unesp.br:11449/205911Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T21:17:33.051474Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
A Berestycki-Lions' type result to a quasilinear elliptic problem involving the 1-Laplacian operator |
title |
A Berestycki-Lions' type result to a quasilinear elliptic problem involving the 1-Laplacian operator |
spellingShingle |
A Berestycki-Lions' type result to a quasilinear elliptic problem involving the 1-Laplacian operator Ortiz Chata, Juan C. [UNESP] 1-Laplacian operator Bounded variation functions Pohozaev identity |
title_short |
A Berestycki-Lions' type result to a quasilinear elliptic problem involving the 1-Laplacian operator |
title_full |
A Berestycki-Lions' type result to a quasilinear elliptic problem involving the 1-Laplacian operator |
title_fullStr |
A Berestycki-Lions' type result to a quasilinear elliptic problem involving the 1-Laplacian operator |
title_full_unstemmed |
A Berestycki-Lions' type result to a quasilinear elliptic problem involving the 1-Laplacian operator |
title_sort |
A Berestycki-Lions' type result to a quasilinear elliptic problem involving the 1-Laplacian operator |
author |
Ortiz Chata, Juan C. [UNESP] |
author_facet |
Ortiz Chata, Juan C. [UNESP] Pimenta, Marcos T.O. [UNESP] |
author_role |
author |
author2 |
Pimenta, Marcos T.O. [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Ortiz Chata, Juan C. [UNESP] Pimenta, Marcos T.O. [UNESP] |
dc.subject.por.fl_str_mv |
1-Laplacian operator Bounded variation functions Pohozaev identity |
topic |
1-Laplacian operator Bounded variation functions Pohozaev identity |
description |
In this work we study a quasilinear elliptic problem involving the 1-Laplacian operator in RN, whose nonlinearity satisfy conditions similar to those ones of the classical work of Berestycki and Lions. Several difficulties are faced when trying to generalize the arguments of the semilinear case, to this quasilinear problem. The main existence theorem is proved through a new version of the well known Mountain Pass Theorem to locally Lipschitz functionals, where it is considered the Cerami compactness condition rather than the Palais-Smale one. It is also proved that all bounded variation solutions which are regular enough, satisfy a Pohozaev type identity. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-06-25T10:23:20Z 2021-06-25T10:23:20Z 2021-08-01 |
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.2021.125074 Journal of Mathematical Analysis and Applications, v. 500, n. 1, 2021. 1096-0813 0022-247X http://hdl.handle.net/11449/205911 10.1016/j.jmaa.2021.125074 2-s2.0-85101176994 |
url |
http://dx.doi.org/10.1016/j.jmaa.2021.125074 http://hdl.handle.net/11449/205911 |
identifier_str_mv |
Journal of Mathematical Analysis and Applications, v. 500, n. 1, 2021. 1096-0813 0022-247X 10.1016/j.jmaa.2021.125074 2-s2.0-85101176994 |
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_ |
1808129306141917184 |