Multiple Solutions for the p ( x ) − Laplace Operator with Critical Growth

Autores
Silva, Analia
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The aim of this paper is to extend previous results regarding the multiplicity of solutions for quasilinear elliptic problems with critical growth to the variable exponent case. We prove, in the spirit of [4], the existence of at least three nontrivial solutions to the quasilinear elliptic equation −Δp(x)u = |u|q(x)−2u + λ f (x, u) in a smooth bounded domain Ω of RN with homogeneous Dirichlet boundary conditions on ∂Ω. We assume that {q(x) = p∗(x)} ≠ ø, where p∗(x) = Np(x)/(N − p(x)) is the critical Sobolev exponent for variable exponents and Δp(x)u = div(|∇u|p(x)−2∇u) is the p(x)−laplacian. The proof is based on variational arguments and the extension of concentration compactness method for variable exponent spaces.
Fil: Silva, Analia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
Concentration-Compactness Principle
Variable Exponent Spaces
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/14926
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/14926
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Multiple Solutions for the p ( x ) − Laplace Operator with Critical GrowthSilva, AnaliaConcentration-Compactness PrincipleVariable Exponent Spaceshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The aim of this paper is to extend previous results regarding the multiplicity of solutions for quasilinear elliptic problems with critical growth to the variable exponent case. We prove, in the spirit of [4], the existence of at least three nontrivial solutions to the quasilinear elliptic equation −Δp(x)u = |u|q(x)−2u + λ f (x, u) in a smooth bounded domain Ω of RN with homogeneous Dirichlet boundary conditions on ∂Ω. We assume that {q(x) = p∗(x)} ≠ ø, where p∗(x) = Np(x)/(N − p(x)) is the critical Sobolev exponent for variable exponents and Δp(x)u = div(|∇u|p(x)−2∇u) is the p(x)−laplacian. The proof is based on variational arguments and the extension of concentration compactness method for variable exponent spaces.Fil: Silva, Analia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaAdvanced Nonlinear Studies, Inc2011-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/14926Silva, Analia; Multiple Solutions for the p ( x ) − Laplace Operator with Critical Growth; Advanced Nonlinear Studies, Inc; Advanced Nonlinear Studies; 11; 1; 1-2011; 63-751536-1365enginfo:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/ans.2011.11.issue-1/ans-2011-0103/ans-2011-0103.xmlinfo:eu-repo/semantics/altIdentifier/doi/10.1515/ans-2011-0103info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:12:15Zoai:ri.conicet.gov.ar:11336/14926instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:12:15.55CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Multiple Solutions for the p ( x ) − Laplace Operator with Critical Growth
title Multiple Solutions for the p ( x ) − Laplace Operator with Critical Growth
spellingShingle Multiple Solutions for the p ( x ) − Laplace Operator with Critical Growth
Silva, Analia
Concentration-Compactness Principle
Variable Exponent Spaces
title_short Multiple Solutions for the p ( x ) − Laplace Operator with Critical Growth
title_full Multiple Solutions for the p ( x ) − Laplace Operator with Critical Growth
title_fullStr Multiple Solutions for the p ( x ) − Laplace Operator with Critical Growth
title_full_unstemmed Multiple Solutions for the p ( x ) − Laplace Operator with Critical Growth
title_sort Multiple Solutions for the p ( x ) − Laplace Operator with Critical Growth
dc.creator.none.fl_str_mv Silva, Analia
author Silva, Analia
author_facet Silva, Analia
author_role author
dc.subject.none.fl_str_mv Concentration-Compactness Principle
Variable Exponent Spaces
topic Concentration-Compactness Principle
Variable Exponent Spaces
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The aim of this paper is to extend previous results regarding the multiplicity of solutions for quasilinear elliptic problems with critical growth to the variable exponent case. We prove, in the spirit of [4], the existence of at least three nontrivial solutions to the quasilinear elliptic equation −Δp(x)u = |u|q(x)−2u + λ f (x, u) in a smooth bounded domain Ω of RN with homogeneous Dirichlet boundary conditions on ∂Ω. We assume that {q(x) = p∗(x)} ≠ ø, where p∗(x) = Np(x)/(N − p(x)) is the critical Sobolev exponent for variable exponents and Δp(x)u = div(|∇u|p(x)−2∇u) is the p(x)−laplacian. The proof is based on variational arguments and the extension of concentration compactness method for variable exponent spaces.
Fil: Silva, Analia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description The aim of this paper is to extend previous results regarding the multiplicity of solutions for quasilinear elliptic problems with critical growth to the variable exponent case. We prove, in the spirit of [4], the existence of at least three nontrivial solutions to the quasilinear elliptic equation −Δp(x)u = |u|q(x)−2u + λ f (x, u) in a smooth bounded domain Ω of RN with homogeneous Dirichlet boundary conditions on ∂Ω. We assume that {q(x) = p∗(x)} ≠ ø, where p∗(x) = Np(x)/(N − p(x)) is the critical Sobolev exponent for variable exponents and Δp(x)u = div(|∇u|p(x)−2∇u) is the p(x)−laplacian. The proof is based on variational arguments and the extension of concentration compactness method for variable exponent spaces.
publishDate 2011
dc.date.none.fl_str_mv 2011-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/14926
Silva, Analia; Multiple Solutions for the p ( x ) − Laplace Operator with Critical Growth; Advanced Nonlinear Studies, Inc; Advanced Nonlinear Studies; 11; 1; 1-2011; 63-75
1536-1365
url http://hdl.handle.net/11336/14926
identifier_str_mv Silva, Analia; Multiple Solutions for the p ( x ) − Laplace Operator with Critical Growth; Advanced Nonlinear Studies, Inc; Advanced Nonlinear Studies; 11; 1; 1-2011; 63-75
1536-1365
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/ans.2011.11.issue-1/ans-2011-0103/ans-2011-0103.xml
info:eu-repo/semantics/altIdentifier/doi/10.1515/ans-2011-0103
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Advanced Nonlinear Studies, Inc
publisher.none.fl_str_mv Advanced Nonlinear Studies, Inc
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1844614028391874560
score 13.070432

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