The asymptotic behavior of constant sign and nodal solutions of (p,q)-Laplacian problems as p goes to 1

Bibliographic Details
Main Author: Figueiredo, Giovany M.
Publication Date: 2025
Other Authors: Pimenta, Marcos T.O. [UNESP], Winkert, Patrick
Format: Article
Language: eng
Source: Repositório Institucional da UNESP
Download full: http://dx.doi.org/10.1016/j.na.2024.113677
https://hdl.handle.net/11449/297339
Summary: In this paper we study the asymptotic behavior of solutions to the (p,q)-equation [Formula presented]has at least two constant sign solutions and one sign-changing solution, whereby the sign-changing solution has least energy among all sign-changing solutions. Furthermore, the solutions belong to the usual Sobolev space W01,q(Ω) which is in contrast with the case of 1-Laplacian problems, where the solutions just belong to the space BV(Ω) of all functions of bounded variation. As far as we know this is the first work dealing with (1,q)-Laplace problems even in the direction of constant sign solutions.
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spelling The asymptotic behavior of constant sign and nodal solutions of (p,q)-Laplacian problems as p goes to 11-laplacianAsymptotic behaviorFunctions of bounded variationp goes to 1Sign-changing solutionsIn this paper we study the asymptotic behavior of solutions to the (p,q)-equation [Formula presented]has at least two constant sign solutions and one sign-changing solution, whereby the sign-changing solution has least energy among all sign-changing solutions. Furthermore, the solutions belong to the usual Sobolev space W01,q(Ω) which is in contrast with the case of 1-Laplacian problems, where the solutions just belong to the space BV(Ω) of all functions of bounded variation. As far as we know this is the first work dealing with (1,q)-Laplace problems even in the direction of constant sign solutions.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Apoio à Pesquisa do Distrito FederalFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Departamento de Matemática Universidade de Brasília - UnB, CEP: 70910-900, Brasília-DFDepartamento de Matemática e Computação Universidade Estadual Paulista - Unesp, CEP: 19060-900, Presidente Prudente - SPTechnische Universität Berlin Institut für Mathematik, Straße des 17. Juni 136Departamento de Matemática e Computação Universidade Estadual Paulista - Unesp, CEP: 19060-900, Presidente Prudente - SPFAPESP: 2023/06617-1FAPESP: 2023/10287-7CNPq: 304765/2021-0Universidade de Brasília (UnB)Universidade Estadual Paulista (UNESP)Institut für MathematikFigueiredo, Giovany M.Pimenta, Marcos T.O. [UNESP]Winkert, Patrick2025-04-29T18:06:17Z2025-02-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.na.2024.113677Nonlinear Analysis, Theory, Methods and Applications, v. 251.0362-546Xhttps://hdl.handle.net/11449/29733910.1016/j.na.2024.1136772-s2.0-85205307901Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengNonlinear Analysis, Theory, Methods and Applicationsinfo:eu-repo/semantics/openAccess2025-04-30T14:28:20Zoai:repositorio.unesp.br:11449/297339Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462025-04-30T14:28:20Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv The asymptotic behavior of constant sign and nodal solutions of (p,q)-Laplacian problems as p goes to 1
title The asymptotic behavior of constant sign and nodal solutions of (p,q)-Laplacian problems as p goes to 1
spellingShingle The asymptotic behavior of constant sign and nodal solutions of (p,q)-Laplacian problems as p goes to 1
Figueiredo, Giovany M.
1-laplacian
Asymptotic behavior
Functions of bounded variation
p goes to 1
Sign-changing solutions
title_short The asymptotic behavior of constant sign and nodal solutions of (p,q)-Laplacian problems as p goes to 1
title_full The asymptotic behavior of constant sign and nodal solutions of (p,q)-Laplacian problems as p goes to 1
title_fullStr The asymptotic behavior of constant sign and nodal solutions of (p,q)-Laplacian problems as p goes to 1
title_full_unstemmed The asymptotic behavior of constant sign and nodal solutions of (p,q)-Laplacian problems as p goes to 1
title_sort The asymptotic behavior of constant sign and nodal solutions of (p,q)-Laplacian problems as p goes to 1
author Figueiredo, Giovany M.
author_facet Figueiredo, Giovany M.
Pimenta, Marcos T.O. [UNESP]
Winkert, Patrick
author_role author
author2 Pimenta, Marcos T.O. [UNESP]
Winkert, Patrick
author2_role author
author
dc.contributor.none.fl_str_mv Universidade de Brasília (UnB)
Universidade Estadual Paulista (UNESP)
Institut für Mathematik
dc.contributor.author.fl_str_mv Figueiredo, Giovany M.
Pimenta, Marcos T.O. [UNESP]
Winkert, Patrick
dc.subject.por.fl_str_mv 1-laplacian
Asymptotic behavior
Functions of bounded variation
p goes to 1
Sign-changing solutions
topic 1-laplacian
Asymptotic behavior
Functions of bounded variation
p goes to 1
Sign-changing solutions
description In this paper we study the asymptotic behavior of solutions to the (p,q)-equation [Formula presented]has at least two constant sign solutions and one sign-changing solution, whereby the sign-changing solution has least energy among all sign-changing solutions. Furthermore, the solutions belong to the usual Sobolev space W01,q(Ω) which is in contrast with the case of 1-Laplacian problems, where the solutions just belong to the space BV(Ω) of all functions of bounded variation. As far as we know this is the first work dealing with (1,q)-Laplace problems even in the direction of constant sign solutions.
publishDate 2025
dc.date.none.fl_str_mv 2025-04-29T18:06:17Z
2025-02-01
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.na.2024.113677
Nonlinear Analysis, Theory, Methods and Applications, v. 251.
0362-546X
https://hdl.handle.net/11449/297339
10.1016/j.na.2024.113677
2-s2.0-85205307901
url http://dx.doi.org/10.1016/j.na.2024.113677
https://hdl.handle.net/11449/297339
identifier_str_mv Nonlinear Analysis, Theory, Methods and Applications, v. 251.
0362-546X
10.1016/j.na.2024.113677
2-s2.0-85205307901
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Nonlinear Analysis, Theory, Methods 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 repositoriounesp@unesp.br
_version_ 1834482960465657856

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