A Nonlocal Operator Breaking the Keller-Osserman Condition

Autores
Ferreira, Raúl; Pérez Pérez, Maria Teresa
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This work is concerned about the existence of solutions to the nonlocal semilinear problem - N J (x - y) (u (y) - u (x)) y + h (u (x)) = f (x) x ω u = g x N ω, (-) R N J(x-y)(u(y)-u(x%)), dy+h (u(x)) = f(x),& ω u=g, x R N ω. verifying that lim x → ω x ω u (x) = + ∞ known in the literature as large solutions. We find out that the relation between the diffusion and the absorption term is not enough to ensure such existence, not even assuming that the boundary datum g blows up close to ω. On the contrary, the role to obtain large solutions is played only by the interior source f, which gives rise to large solutions even without the presence of the absorption. We determine necessary and sufficient conditions on f providing large solutions and compute the blow-up rates of such solutions in terms of h and f. Finally, we also study the uniqueness of large solutions.
Fil: Ferreira, Raúl. Universidad Complutense de Madrid; España
Fil: Pérez Pérez, Maria Teresa. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
KELLER-OSSERMAN CONDITION
LARGE SOLUTIONS
NONLOCAL DIFFUSION
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:11336/55505
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/55505
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A Nonlocal Operator Breaking the Keller-Osserman ConditionFerreira, RaúlPérez Pérez, Maria TeresaKELLER-OSSERMAN CONDITIONLARGE SOLUTIONSNONLOCAL DIFFUSIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This work is concerned about the existence of solutions to the nonlocal semilinear problem - N J (x - y) (u (y) - u (x)) y + h (u (x)) = f (x) x ω u = g x N ω, (-) R N J(x-y)(u(y)-u(x%)), dy+h (u(x)) = f(x),& ω u=g, x R N ω. verifying that lim x → ω x ω u (x) = + ∞ known in the literature as large solutions. We find out that the relation between the diffusion and the absorption term is not enough to ensure such existence, not even assuming that the boundary datum g blows up close to ω. On the contrary, the role to obtain large solutions is played only by the interior source f, which gives rise to large solutions even without the presence of the absorption. We determine necessary and sufficient conditions on f providing large solutions and compute the blow-up rates of such solutions in terms of h and f. Finally, we also study the uniqueness of large solutions.Fil: Ferreira, Raúl. Universidad Complutense de Madrid; EspañaFil: Pérez Pérez, Maria Teresa. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaDe Gruyter2017-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/55505Ferreira, Raúl; Pérez Pérez, Maria Teresa; A Nonlocal Operator Breaking the Keller-Osserman Condition; De Gruyter; Advanced Nonlinear Studies; 17; 4; 10-2017; 715-7251536-1365CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/ans.2017.17.issue-4/ans-2016-6011/ans-2016-6011.xmlinfo:eu-repo/semantics/altIdentifier/doi/10.1515/ans-2016-6011info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:03:48Zoai:ri.conicet.gov.ar:11336/55505instacron: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:34982025-09-03 10:03:48.242CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A Nonlocal Operator Breaking the Keller-Osserman Condition
title A Nonlocal Operator Breaking the Keller-Osserman Condition
spellingShingle A Nonlocal Operator Breaking the Keller-Osserman Condition
Ferreira, Raúl
KELLER-OSSERMAN CONDITION
LARGE SOLUTIONS
NONLOCAL DIFFUSION
title_short A Nonlocal Operator Breaking the Keller-Osserman Condition
title_full A Nonlocal Operator Breaking the Keller-Osserman Condition
title_fullStr A Nonlocal Operator Breaking the Keller-Osserman Condition
title_full_unstemmed A Nonlocal Operator Breaking the Keller-Osserman Condition
title_sort A Nonlocal Operator Breaking the Keller-Osserman Condition
dc.creator.none.fl_str_mv Ferreira, Raúl
Pérez Pérez, Maria Teresa
author Ferreira, Raúl
author_facet Ferreira, Raúl
Pérez Pérez, Maria Teresa
author_role author
author2 Pérez Pérez, Maria Teresa
author2_role author
dc.subject.none.fl_str_mv KELLER-OSSERMAN CONDITION
LARGE SOLUTIONS
NONLOCAL DIFFUSION
topic KELLER-OSSERMAN CONDITION
LARGE SOLUTIONS
NONLOCAL DIFFUSION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This work is concerned about the existence of solutions to the nonlocal semilinear problem - N J (x - y) (u (y) - u (x)) y + h (u (x)) = f (x) x ω u = g x N ω, (-) R N J(x-y)(u(y)-u(x%)), dy+h (u(x)) = f(x),& ω u=g, x R N ω. verifying that lim x → ω x ω u (x) = + ∞ known in the literature as large solutions. We find out that the relation between the diffusion and the absorption term is not enough to ensure such existence, not even assuming that the boundary datum g blows up close to ω. On the contrary, the role to obtain large solutions is played only by the interior source f, which gives rise to large solutions even without the presence of the absorption. We determine necessary and sufficient conditions on f providing large solutions and compute the blow-up rates of such solutions in terms of h and f. Finally, we also study the uniqueness of large solutions.
Fil: Ferreira, Raúl. Universidad Complutense de Madrid; España
Fil: Pérez Pérez, Maria Teresa. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description This work is concerned about the existence of solutions to the nonlocal semilinear problem - N J (x - y) (u (y) - u (x)) y + h (u (x)) = f (x) x ω u = g x N ω, (-) R N J(x-y)(u(y)-u(x%)), dy+h (u(x)) = f(x),& ω u=g, x R N ω. verifying that lim x → ω x ω u (x) = + ∞ known in the literature as large solutions. We find out that the relation between the diffusion and the absorption term is not enough to ensure such existence, not even assuming that the boundary datum g blows up close to ω. On the contrary, the role to obtain large solutions is played only by the interior source f, which gives rise to large solutions even without the presence of the absorption. We determine necessary and sufficient conditions on f providing large solutions and compute the blow-up rates of such solutions in terms of h and f. Finally, we also study the uniqueness of large solutions.
publishDate 2017
dc.date.none.fl_str_mv 2017-10
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/11336/55505
Ferreira, Raúl; Pérez Pérez, Maria Teresa; A Nonlocal Operator Breaking the Keller-Osserman Condition; De Gruyter; Advanced Nonlinear Studies; 17; 4; 10-2017; 715-725
1536-1365
CONICET Digital
CONICET
url http://hdl.handle.net/11336/55505
identifier_str_mv Ferreira, Raúl; Pérez Pérez, Maria Teresa; A Nonlocal Operator Breaking the Keller-Osserman Condition; De Gruyter; Advanced Nonlinear Studies; 17; 4; 10-2017; 715-725
1536-1365
CONICET Digital
CONICET
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.2017.17.issue-4/ans-2016-6011/ans-2016-6011.xml
info:eu-repo/semantics/altIdentifier/doi/10.1515/ans-2016-6011
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 De Gruyter
publisher.none.fl_str_mv De Gruyter
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
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score 12.885934

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