Semilinear problems for the fractional laplacian with a singular nonlinearity

The aim of this paper is to study the solvability of the problem (-Δ)s u = F(x,u) := λ f(x)/uγ + Mup in ω u > 0 in ω, u = 0 in RN \ ω, where Ω is a bounded smooth domain of RN, N > 2s, M ε {0, 1}, 0 < s < 1, γ > 0, λ > 0, p > 1 and f is a nonnegative function. We distinguish two...

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Authors: Barrios, B., De Bonis, I., Medina de ja Torre, María, Peral Alonso, Ireneo
Format: article
Publication Date:2015
Country:España
Institution:Universidad Autónoma de Madrid
Repository:Biblos-e Archivo. Repositorio Institucional de la UAM
Language:English
OAI Identifier:oai:repositorio.uam.es:10486/676397
Online Access:http://hdl.handle.net/10486/676397
https://dx.doi.org/10.1515/math-2015-0038
Access Level:Open access
Keyword:Existence and multiplicity
Fractional Laplacian
Solvability of elliptic equations
Matemáticas
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spelling Semilinear problems for the fractional laplacian with a singular nonlinearityBarrios, B.De Bonis, I.Medina de ja Torre, MaríaPeral Alonso, IreneoExistence and multiplicityFractional LaplacianSolvability of elliptic equationsMatemáticasThe aim of this paper is to study the solvability of the problem (-Δ)s u = F(x,u) := λ f(x)/uγ + Mup in ω u > 0 in ω, u = 0 in RN \ ω, where Ω is a bounded smooth domain of RN, N > 2s, M ε {0, 1}, 0 < s < 1, γ > 0, λ > 0, p > 1 and f is a nonnegative function. We distinguish two cases: - For M = 0, we prove the existence of a solution for every γ > 0 and λ > 0. A1 - For M = 1, we consider f ≡ 1 and we find a threshold ∧ such that there exists a solution for every 0 < λ < ∧, and there does not for λ > ∧Work partially supported by project MTM2013-40846-P MINECO. The third author is also supported for the grant BES-2011-044216 associated to MTM2010-18128De Gruyter Open LtdDepartamento de MatemáticasFacultad de Ciencias20152015-05-28research articlehttp://purl.org/coar/resource_type/c_2df8fbb1VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/676397https://dx.doi.org/10.1515/math-2015-0038reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/6763972026-06-23T12:46:27Z
dc.title.none.fl_str_mv Semilinear problems for the fractional laplacian with a singular nonlinearity
title Semilinear problems for the fractional laplacian with a singular nonlinearity
spellingShingle Semilinear problems for the fractional laplacian with a singular nonlinearity
Barrios, B.
Existence and multiplicity
Fractional Laplacian
Solvability of elliptic equations
Matemáticas
title_short Semilinear problems for the fractional laplacian with a singular nonlinearity
title_full Semilinear problems for the fractional laplacian with a singular nonlinearity
title_fullStr Semilinear problems for the fractional laplacian with a singular nonlinearity
title_full_unstemmed Semilinear problems for the fractional laplacian with a singular nonlinearity
title_sort Semilinear problems for the fractional laplacian with a singular nonlinearity
dc.creator.none.fl_str_mv Barrios, B.
De Bonis, I.
Medina de ja Torre, María
Peral Alonso, Ireneo
author Barrios, B.
author_facet Barrios, B.
De Bonis, I.
Medina de ja Torre, María
Peral Alonso, Ireneo
author_role author
author2 De Bonis, I.
Medina de ja Torre, María
Peral Alonso, Ireneo
author2_role author
author
author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
dc.subject.none.fl_str_mv Existence and multiplicity
Fractional Laplacian
Solvability of elliptic equations
Matemáticas
topic Existence and multiplicity
Fractional Laplacian
Solvability of elliptic equations
Matemáticas
description The aim of this paper is to study the solvability of the problem (-Δ)s u = F(x,u) := λ f(x)/uγ + Mup in ω u > 0 in ω, u = 0 in RN \ ω, where Ω is a bounded smooth domain of RN, N > 2s, M ε {0, 1}, 0 < s < 1, γ > 0, λ > 0, p > 1 and f is a nonnegative function. We distinguish two cases: - For M = 0, we prove the existence of a solution for every γ > 0 and λ > 0. A1 - For M = 1, we consider f ≡ 1 and we find a threshold ∧ such that there exists a solution for every 0 < λ < ∧, and there does not for λ > ∧
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-05-28
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10486/676397
https://dx.doi.org/10.1515/math-2015-0038
url http://hdl.handle.net/10486/676397
https://dx.doi.org/10.1515/math-2015-0038
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 De Gruyter Open Ltd
publisher.none.fl_str_mv De Gruyter Open Ltd
dc.source.none.fl_str_mv reponame:Biblos-e Archivo. Repositorio Institucional de la UAM
instname:Universidad Autónoma de Madrid
instname_str Universidad Autónoma de Madrid
reponame_str Biblos-e Archivo. Repositorio Institucional de la UAM
collection Biblos-e Archivo. Repositorio Institucional de la UAM
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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