A convex-concave problem with a nonlinear boundary condition

Autores
Garcia-Azorero, J.; Peral, I.; Rossi, J.D.
Año de publicación
2004
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we study the existence of nontrivial solutions of the problem {-Δu+u = u p-2u in Ω, {∂u/∂v = λ u q-2u on ∂Ω, with 1<q<2(N-1)/(N-2) and 1<p≤2N/(N-2). In the concave-convex case, i.e., 1<q<2<p, if λ is small there exist two positive solutions while for λ large there is no positive solution. When p is critical, and q subcritical we obtain existence results using the concentration compactness method. Finally, we apply the implicit function theorem to obtain solutions for λ small near u0 = 1. © 2003 Elsevier Science (USA). All rights reserved.
Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente
J. Differ. Equ. 2004;198(1):91-128
Materia
Critical exponents
Nonlinear boundary conditions
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_00220396_v198_n1_p91_GarciaAzorero

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oai_identifier_str paperaa:paper_00220396_v198_n1_p91_GarciaAzorero
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repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling A convex-concave problem with a nonlinear boundary conditionGarcia-Azorero, J.Peral, I.Rossi, J.D.Critical exponentsNonlinear boundary conditionsIn this paper we study the existence of nontrivial solutions of the problem {-Δu+u = u p-2u in Ω, {∂u/∂v = λ u q-2u on ∂Ω, with 1&lt;q&lt;2(N-1)/(N-2) and 1&lt;p≤2N/(N-2). In the concave-convex case, i.e., 1&lt;q&lt;2&lt;p, if λ is small there exist two positive solutions while for λ large there is no positive solution. When p is critical, and q subcritical we obtain existence results using the concentration compactness method. Finally, we apply the implicit function theorem to obtain solutions for λ small near u0 = 1. © 2003 Elsevier Science (USA). All rights reserved.Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2004info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p91_GarciaAzoreroJ. Differ. Equ. 2004;198(1):91-128reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-09-29T13:43:05Zpaperaa:paper_00220396_v198_n1_p91_GarciaAzoreroInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-09-29 13:43:07.219Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv A convex-concave problem with a nonlinear boundary condition
title A convex-concave problem with a nonlinear boundary condition
spellingShingle A convex-concave problem with a nonlinear boundary condition
Garcia-Azorero, J.
Critical exponents
Nonlinear boundary conditions
title_short A convex-concave problem with a nonlinear boundary condition
title_full A convex-concave problem with a nonlinear boundary condition
title_fullStr A convex-concave problem with a nonlinear boundary condition
title_full_unstemmed A convex-concave problem with a nonlinear boundary condition
title_sort A convex-concave problem with a nonlinear boundary condition
dc.creator.none.fl_str_mv Garcia-Azorero, J.
Peral, I.
Rossi, J.D.
author Garcia-Azorero, J.
author_facet Garcia-Azorero, J.
Peral, I.
Rossi, J.D.
author_role author
author2 Peral, I.
Rossi, J.D.
author2_role author
author
dc.subject.none.fl_str_mv Critical exponents
Nonlinear boundary conditions
topic Critical exponents
Nonlinear boundary conditions
dc.description.none.fl_txt_mv In this paper we study the existence of nontrivial solutions of the problem {-Δu+u = u p-2u in Ω, {∂u/∂v = λ u q-2u on ∂Ω, with 1&lt;q&lt;2(N-1)/(N-2) and 1&lt;p≤2N/(N-2). In the concave-convex case, i.e., 1&lt;q&lt;2&lt;p, if λ is small there exist two positive solutions while for λ large there is no positive solution. When p is critical, and q subcritical we obtain existence results using the concentration compactness method. Finally, we apply the implicit function theorem to obtain solutions for λ small near u0 = 1. © 2003 Elsevier Science (USA). All rights reserved.
Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
description In this paper we study the existence of nontrivial solutions of the problem {-Δu+u = u p-2u in Ω, {∂u/∂v = λ u q-2u on ∂Ω, with 1&lt;q&lt;2(N-1)/(N-2) and 1&lt;p≤2N/(N-2). In the concave-convex case, i.e., 1&lt;q&lt;2&lt;p, if λ is small there exist two positive solutions while for λ large there is no positive solution. When p is critical, and q subcritical we obtain existence results using the concentration compactness method. Finally, we apply the implicit function theorem to obtain solutions for λ small near u0 = 1. © 2003 Elsevier Science (USA). All rights reserved.
publishDate 2004
dc.date.none.fl_str_mv 2004
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p91_GarciaAzorero
url http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p91_GarciaAzorero
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
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eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv J. Differ. Equ. 2004;198(1):91-128
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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