On the number and Indices of equilibria in a space-dependent bistable equation

We study a singular perturbation problem of a piecewise autonomous bistable equation. We give sufficient conditions both for the boundedness and the unboundedness of the number and Morse index of its equilibrium solutions as the perturbation parameter approaches zero. For the bounded case, we provid...

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Detalhes bibliográficos
Autores: Salazar, Domingo, Solà-Morales Rubió, Joan de|||0000-0003-2896-2917
Formato: artículo
Fecha de publicación:1999
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/1210
Acesso em linha:https://hdl.handle.net/2117/1210
Access Level:acceso abierto
Palavra-chave:Differentiable dynamical systems
Partial differential equations
Parabolic partial differential equations
space-dependent bistable equation
Sistemes dinàmics diferenciables
Equacions en derivades parcials
Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions
Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems
Classificació AMS::37 Dynamical systems and ergodic theory::37L Infinite-dimensional dissipative dynamical systems
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spelling On the number and Indices of equilibria in a space-dependent bistable equationSalazar, DomingoSolà-Morales Rubió, Joan de|||0000-0003-2896-2917Differentiable dynamical systemsPartial differential equationsParabolic partial differential equationsspace-dependent bistable equationSistemes dinàmics diferenciablesEquacions en derivades parcialsClassificació AMS::35 Partial differential equations::35B Qualitative properties of solutionsClassificació AMS::35 Partial differential equations::35K Parabolic equations and systemsClassificació AMS::37 Dynamical systems and ergodic theory::37L Infinite-dimensional dissipative dynamical systemsWe study a singular perturbation problem of a piecewise autonomous bistable equation. We give sufficient conditions both for the boundedness and the unboundedness of the number and Morse index of its equilibrium solutions as the perturbation parameter approaches zero. For the bounded case, we provide the number of equilibria as a function of the number of discontinuities of the reaction term.19991999-01-0120072007-10-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/1210reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 2.5 Spainhttp://creativecommons.org/licenses/by-nc-nd/2.5/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/12102026-05-27T15:37:01Z
dc.title.none.fl_str_mv On the number and Indices of equilibria in a space-dependent bistable equation
title On the number and Indices of equilibria in a space-dependent bistable equation
spellingShingle On the number and Indices of equilibria in a space-dependent bistable equation
Salazar, Domingo
Differentiable dynamical systems
Partial differential equations
Parabolic partial differential equations
space-dependent bistable equation
Sistemes dinàmics diferenciables
Equacions en derivades parcials
Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions
Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems
Classificació AMS::37 Dynamical systems and ergodic theory::37L Infinite-dimensional dissipative dynamical systems
title_short On the number and Indices of equilibria in a space-dependent bistable equation
title_full On the number and Indices of equilibria in a space-dependent bistable equation
title_fullStr On the number and Indices of equilibria in a space-dependent bistable equation
title_full_unstemmed On the number and Indices of equilibria in a space-dependent bistable equation
title_sort On the number and Indices of equilibria in a space-dependent bistable equation
dc.creator.none.fl_str_mv Salazar, Domingo
Solà-Morales Rubió, Joan de|||0000-0003-2896-2917
author Salazar, Domingo
author_facet Salazar, Domingo
Solà-Morales Rubió, Joan de|||0000-0003-2896-2917
author_role author
author2 Solà-Morales Rubió, Joan de|||0000-0003-2896-2917
author2_role author
dc.subject.none.fl_str_mv Differentiable dynamical systems
Partial differential equations
Parabolic partial differential equations
space-dependent bistable equation
Sistemes dinàmics diferenciables
Equacions en derivades parcials
Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions
Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems
Classificació AMS::37 Dynamical systems and ergodic theory::37L Infinite-dimensional dissipative dynamical systems
topic Differentiable dynamical systems
Partial differential equations
Parabolic partial differential equations
space-dependent bistable equation
Sistemes dinàmics diferenciables
Equacions en derivades parcials
Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions
Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems
Classificació AMS::37 Dynamical systems and ergodic theory::37L Infinite-dimensional dissipative dynamical systems
description We study a singular perturbation problem of a piecewise autonomous bistable equation. We give sufficient conditions both for the boundedness and the unboundedness of the number and Morse index of its equilibrium solutions as the perturbation parameter approaches zero. For the bounded case, we provide the number of equilibria as a function of the number of discontinuities of the reaction term.
publishDate 1999
dc.date.none.fl_str_mv 1999
1999-01-01
2007
2007-10-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/1210
url https://hdl.handle.net/2117/1210
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
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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