The competition between incoming and outgoing fluxes in an elliptic problem

In this work we consider existence and uniqueness of positive solutions to the elliptic equation −∆u = λu in Ω, with the nonlinear boundary conditions ∂u ∂ν = u p on Γ1, ∂u ∂ν = −u q on Γ2, where Ω is a smooth bounded domain, ∂Ω = Γ1 ∪ Γ2, Γ1 ∩ Γ2 = ∅, ν is the outward unit normal, p, q > 0 and λ...

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Autores: García Melián, Jorge José, Rossi Pérez, Julio Daniel, Suárez Fernández, Antonio
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2007
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/40060
Acceso en línea:http://hdl.handle.net/11441/40060
https://doi.org/10.1142/S0219199707002642
Access Level:acceso abierto
Palabra clave:Elliptic problems
nonlinear boundary conditions
sub and supersolutions
bifurcation
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spelling The competition between incoming and outgoing fluxes in an elliptic problemGarcía Melián, Jorge JoséRossi Pérez, Julio DanielSuárez Fernández, AntonioElliptic problemsnonlinear boundary conditionssub and supersolutionsbifurcationIn this work we consider existence and uniqueness of positive solutions to the elliptic equation −∆u = λu in Ω, with the nonlinear boundary conditions ∂u ∂ν = u p on Γ1, ∂u ∂ν = −u q on Γ2, where Ω is a smooth bounded domain, ∂Ω = Γ1 ∪ Γ2, Γ1 ∩ Γ2 = ∅, ν is the outward unit normal, p, q > 0 and λ is a real parameter. We obtain a complete picture of the bifurcation diagram of the problem, depending on the values of p, q and the parameter λ. Our proofs are based on different techniques: variational arguments, bifurcation techniques or comparison arguments, depending on the range of parameters considered.Ministerio de Educación y CienciaFondo Europeo de Desarrollo RegionalWorld ScientificEcuaciones Diferenciales y Análisis NuméricoMinisterio de Educación y Ciencia (MEC). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)2007info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/40060https://doi.org/10.1142/S0219199707002642reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésCommunications in Contemporary Mathematics, 9 (6), 781-810.MTM2005-06480BFM 2003-06446MTM2006-07932ANPCyT PICThttp://dx.doi.org/10.1142/S0219199707002642info:eu-repo/semantics/openAccessoai:idus.us.es:11441/400602026-06-17T12:51:07Z
dc.title.none.fl_str_mv The competition between incoming and outgoing fluxes in an elliptic problem
title The competition between incoming and outgoing fluxes in an elliptic problem
spellingShingle The competition between incoming and outgoing fluxes in an elliptic problem
García Melián, Jorge José
Elliptic problems
nonlinear boundary conditions
sub and supersolutions
bifurcation
title_short The competition between incoming and outgoing fluxes in an elliptic problem
title_full The competition between incoming and outgoing fluxes in an elliptic problem
title_fullStr The competition between incoming and outgoing fluxes in an elliptic problem
title_full_unstemmed The competition between incoming and outgoing fluxes in an elliptic problem
title_sort The competition between incoming and outgoing fluxes in an elliptic problem
dc.creator.none.fl_str_mv García Melián, Jorge José
Rossi Pérez, Julio Daniel
Suárez Fernández, Antonio
author García Melián, Jorge José
author_facet García Melián, Jorge José
Rossi Pérez, Julio Daniel
Suárez Fernández, Antonio
author_role author
author2 Rossi Pérez, Julio Daniel
Suárez Fernández, Antonio
author2_role author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
Ministerio de Educación y Ciencia (MEC). España
European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
dc.subject.none.fl_str_mv Elliptic problems
nonlinear boundary conditions
sub and supersolutions
bifurcation
topic Elliptic problems
nonlinear boundary conditions
sub and supersolutions
bifurcation
description In this work we consider existence and uniqueness of positive solutions to the elliptic equation −∆u = λu in Ω, with the nonlinear boundary conditions ∂u ∂ν = u p on Γ1, ∂u ∂ν = −u q on Γ2, where Ω is a smooth bounded domain, ∂Ω = Γ1 ∪ Γ2, Γ1 ∩ Γ2 = ∅, ν is the outward unit normal, p, q > 0 and λ is a real parameter. We obtain a complete picture of the bifurcation diagram of the problem, depending on the values of p, q and the parameter λ. Our proofs are based on different techniques: variational arguments, bifurcation techniques or comparison arguments, depending on the range of parameters considered.
publishDate 2007
dc.date.none.fl_str_mv 2007
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/40060
https://doi.org/10.1142/S0219199707002642
url http://hdl.handle.net/11441/40060
https://doi.org/10.1142/S0219199707002642
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Communications in Contemporary Mathematics, 9 (6), 781-810.
MTM2005-06480
BFM 2003-06446
MTM2006-07932
ANPCyT PICT
http://dx.doi.org/10.1142/S0219199707002642
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv World Scientific
publisher.none.fl_str_mv World Scientific
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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