Existence and concentration of positive solutions for a critical p&q equation

Detalhes bibliográficos
Autor(a) principal: Costa, Gustavo Silvestre do Amaral
Data de Publicação: 2021
Outros Autores: Figueiredo, Giovany de Jesus Malcher
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UnB
Texto Completo: http://repositorio2.unb.br/jspui/handle/10482/48604
https://doi.org/10.1515/anona-2020-0190
Resumo: We show existence and concentration results for a class of p&q critical problems given by −div a ϵp|∇u| p ϵp|∇u| p−2∇u + V(z)b |u| p |u| p−2u = f(u) + |u| q*−2u in RN , where u ∈ W1,p(RN) ∩ W1,q(RN), ϵ > 0 is a small parameter, 1 < p ≤ q < N, N ≥ 2 and q* = Nq/(N − q). The potential V is positive and f is a superlinear function of C1 class. We use Mountain Pass Theorem and the penalization arguments introduced by Del Pino & Felmer’s associated to Lions’ Concentration and Compactness Principle in order to overcome the lack of compactness.
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spelling Existence and concentration of positive solutions for a critical p&q equationExpoente críticoEquação p&qMétodos variacionaisWe show existence and concentration results for a class of p&q critical problems given by −div a ϵp|∇u| p ϵp|∇u| p−2∇u + V(z)b |u| p |u| p−2u = f(u) + |u| q*−2u in RN , where u ∈ W1,p(RN) ∩ W1,q(RN), ϵ > 0 is a small parameter, 1 < p ≤ q < N, N ≥ 2 and q* = Nq/(N − q). The potential V is positive and f is a superlinear function of C1 class. We use Mountain Pass Theorem and the penalization arguments introduced by Del Pino & Felmer’s associated to Lions’ Concentration and Compactness Principle in order to overcome the lack of compactness.Instituto de Ciências Exatas (IE)Departamento de Matemática (IE MAT)De Gruyter2024-07-08T17:00:23Z2024-07-08T17:00:23Z2021-07-17info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfCOSTA, Gustavo S.; FIGUEIREDO, Giovany M. Existence and concentration of positive solutions for a critical p&q equation. Advances in Nonlinear Analysis, [S. l.], v. 11, n.1, 2, p. 243-267, 2022. DOI: https://doi.org/10.1515/anona-2020-0190. Disponível em:https://www.degruyter.com/document/doi/10.1515/anona-2020-0190/html. Acesso em: 08 jul. 2024.http://repositorio2.unb.br/jspui/handle/10482/48604https://doi.org/10.1515/anona-2020-0190engOpen Access. © 2021 Gustavo S. Costa and Giovany M. Figueiredo, published by De Gruyter. (CC BY) This work is licensed under the Creative Commons Attribution alone 4.0 License.info:eu-repo/semantics/openAccessCosta, Gustavo Silvestre do AmaralFigueiredo, Giovany de Jesus Malcherreponame:Repositório Institucional da UnBinstname:Universidade de Brasília (UnB)instacron:UNB2024-07-08T17:00:23Zoai:repositorio.unb.br:10482/48604Repositório InstitucionalPUBhttps://repositorio.unb.br/oai/requestrepositorio@unb.bropendoar:2024-07-08T17:00:23Repositório Institucional da UnB - Universidade de Brasília (UnB)false
dc.title.none.fl_str_mv Existence and concentration of positive solutions for a critical p&q equation
title Existence and concentration of positive solutions for a critical p&q equation
spellingShingle Existence and concentration of positive solutions for a critical p&q equation
Costa, Gustavo Silvestre do Amaral
Expoente crítico
Equação p&q
Métodos variacionais
title_short Existence and concentration of positive solutions for a critical p&q equation
title_full Existence and concentration of positive solutions for a critical p&q equation
title_fullStr Existence and concentration of positive solutions for a critical p&q equation
title_full_unstemmed Existence and concentration of positive solutions for a critical p&q equation
title_sort Existence and concentration of positive solutions for a critical p&q equation
author Costa, Gustavo Silvestre do Amaral
author_facet Costa, Gustavo Silvestre do Amaral
Figueiredo, Giovany de Jesus Malcher
author_role author
author2 Figueiredo, Giovany de Jesus Malcher
author2_role author
dc.contributor.author.fl_str_mv Costa, Gustavo Silvestre do Amaral
Figueiredo, Giovany de Jesus Malcher
dc.subject.por.fl_str_mv Expoente crítico
Equação p&q
Métodos variacionais
topic Expoente crítico
Equação p&q
Métodos variacionais
description We show existence and concentration results for a class of p&q critical problems given by −div a ϵp|∇u| p ϵp|∇u| p−2∇u + V(z)b |u| p |u| p−2u = f(u) + |u| q*−2u in RN , where u ∈ W1,p(RN) ∩ W1,q(RN), ϵ > 0 is a small parameter, 1 < p ≤ q < N, N ≥ 2 and q* = Nq/(N − q). The potential V is positive and f is a superlinear function of C1 class. We use Mountain Pass Theorem and the penalization arguments introduced by Del Pino & Felmer’s associated to Lions’ Concentration and Compactness Principle in order to overcome the lack of compactness.
publishDate 2021
dc.date.none.fl_str_mv 2021-07-17
2024-07-08T17:00:23Z
2024-07-08T17:00:23Z
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 COSTA, Gustavo S.; FIGUEIREDO, Giovany M. Existence and concentration of positive solutions for a critical p&q equation. Advances in Nonlinear Analysis, [S. l.], v. 11, n.1, 2, p. 243-267, 2022. DOI: https://doi.org/10.1515/anona-2020-0190. Disponível em:https://www.degruyter.com/document/doi/10.1515/anona-2020-0190/html. Acesso em: 08 jul. 2024.
http://repositorio2.unb.br/jspui/handle/10482/48604
https://doi.org/10.1515/anona-2020-0190
identifier_str_mv COSTA, Gustavo S.; FIGUEIREDO, Giovany M. Existence and concentration of positive solutions for a critical p&q equation. Advances in Nonlinear Analysis, [S. l.], v. 11, n.1, 2, p. 243-267, 2022. DOI: https://doi.org/10.1515/anona-2020-0190. Disponível em:https://www.degruyter.com/document/doi/10.1515/anona-2020-0190/html. Acesso em: 08 jul. 2024.
url http://repositorio2.unb.br/jspui/handle/10482/48604
https://doi.org/10.1515/anona-2020-0190
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv De Gruyter
publisher.none.fl_str_mv De Gruyter
dc.source.none.fl_str_mv reponame:Repositório Institucional da UnB
instname:Universidade de Brasília (UnB)
instacron:UNB
instname_str Universidade de Brasília (UnB)
instacron_str UNB
institution UNB
reponame_str Repositório Institucional da UnB
collection Repositório Institucional da UnB
repository.name.fl_str_mv Repositório Institucional da UnB - Universidade de Brasília (UnB)
repository.mail.fl_str_mv repositorio@unb.br
_version_ 1814508278380494848

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