Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity

We consider an elliptic equation with a nonlinear boundary condition which is asymptotically linear at infinity and which depends on a parameter. As the parameter crosses some critical values, there appear certain resonances in the equation producing solutions that bifurcate from infinity. We study...

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Detalles Bibliográficos
Autores: Arrieta Algarra, José María, Pardo San Gil, Rosa María, Rodríguez Bernal, Aníbal
Tipo de recurso: artículo
Fecha de publicación:2007
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/49721
Acceso en línea:https://hdl.handle.net/20.500.14352/49721
Access Level:acceso abierto
Palabra clave:517.9
Reaction-diffusion equations
Parabolic problems
Blow-up
Attractors
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
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spelling Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinityArrieta Algarra, José MaríaPardo San Gil, Rosa MaríaRodríguez Bernal, Aníbal517.9Reaction-diffusion equationsParabolic problemsBlow-upAttractorsEcuaciones diferenciales1202.07 Ecuaciones en DiferenciasWe consider an elliptic equation with a nonlinear boundary condition which is asymptotically linear at infinity and which depends on a parameter. As the parameter crosses some critical values, there appear certain resonances in the equation producing solutions that bifurcate from infinity. We study the bifurcation branches, characterize when they are sub- or supercritical and analyse the stability type of the solutions. Furthermore, we apply these results and techniques to obtain Landesman–Lazer-type conditions guaranteeing the existence of solutions in the resonant case and to obtain an anti-maximum principleCambridge University PressUniversidad Complutense de Madrid20072007-04-0120072007-04-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/49721reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/497212026-06-02T12:44:21Z
dc.title.none.fl_str_mv Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity
title Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity
spellingShingle Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity
Arrieta Algarra, José María
517.9
Reaction-diffusion equations
Parabolic problems
Blow-up
Attractors
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
title_short Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity
title_full Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity
title_fullStr Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity
title_full_unstemmed Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity
title_sort Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity
dc.creator.none.fl_str_mv Arrieta Algarra, José María
Pardo San Gil, Rosa María
Rodríguez Bernal, Aníbal
author Arrieta Algarra, José María
author_facet Arrieta Algarra, José María
Pardo San Gil, Rosa María
Rodríguez Bernal, Aníbal
author_role author
author2 Pardo San Gil, Rosa María
Rodríguez Bernal, Aníbal
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517.9
Reaction-diffusion equations
Parabolic problems
Blow-up
Attractors
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
topic 517.9
Reaction-diffusion equations
Parabolic problems
Blow-up
Attractors
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
description We consider an elliptic equation with a nonlinear boundary condition which is asymptotically linear at infinity and which depends on a parameter. As the parameter crosses some critical values, there appear certain resonances in the equation producing solutions that bifurcate from infinity. We study the bifurcation branches, characterize when they are sub- or supercritical and analyse the stability type of the solutions. Furthermore, we apply these results and techniques to obtain Landesman–Lazer-type conditions guaranteeing the existence of solutions in the resonant case and to obtain an anti-maximum principle
publishDate 2007
dc.date.none.fl_str_mv 2007
2007-04-01
2007
2007-04-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/49721
url https://hdl.handle.net/20.500.14352/49721
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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