Fractional Sobolev space with Riemann–Liouville fractional derivative and application to a fractional concave–convex problem

Descripción del Articulo

This work was partially supported by CONCYTEC PERU, 379-2019-FONDECYT “ASPECTOS CUALITATIVOS DE ECUACIONES NO-LOCALES Y APLICACIONES”
Detalles Bibliográficos
Autores: Ledesma C.E.T., Bonilla M.C.M.
Formato: artículo
Fecha de Publicación:2021
Institución:Consejo Nacional de Ciencia Tecnología e Innovación
Repositorio:CONCYTEC-Institucional
Lenguaje:inglés
OAI Identifier:oai:repositorio.concytec.gob.pe:20.500.12390/3003
Enlace del recurso:https://hdl.handle.net/20.500.12390/3003
https://doi.org/10.1007/s43036-021-00159-w
Nivel de acceso:acceso abierto
Materia:Variational methods
Fractional Riemman–Liouville operators
Fractional Sobolev spaces
Nonlocal problems
https://purl.org/pe-repo/ocde/ford#1.01.02
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spelling Publicationrp08575600rp08576600Ledesma C.E.T.Bonilla M.C.M.2024-05-30T23:13:38Z2024-05-30T23:13:38Z2021https://hdl.handle.net/20.500.12390/3003https://doi.org/10.1007/s43036-021-00159-w2-s2.0-85112786087This work was partially supported by CONCYTEC PERU, 379-2019-FONDECYT “ASPECTOS CUALITATIVOS DE ECUACIONES NO-LOCALES Y APLICACIONES”A new fractional function space EL?[a,b] with Riemann–Liouville fractional derivative and its related properties are established in this paper. Under this configuration, the following fractional concave–convex problem: xDb?(aDx?u)=?u?+up,in(a,b)B?(u)=0,in?(a,b)where ?? (0 , 1) , ?? (0 , 1) and p?(1,1+2?1-2?) if ??(0,12) and p? (1 , + ?) if ??(12,1). B?(u) represent the boundary condition of the problem which depend of the behavior of ?? (0 , 1) , that is: B?(u)={limx?a+aIx1-?u(x)=0,if??(0,12)u(a)=u(b)=0,if??(12,1).By using Ekeland’s variational principle and mountain pass theorem we show that the problem (0.1) at less has two nontrivial weak solutions. © 2021, Tusi Mathematical Research Group (TMRG).Consejo Nacional de Ciencia, Tecnología e Innovación Tecnológica - ConcytecengBirkhauserAdvances in Operator Theoryinfo:eu-repo/semantics/openAccessVariational methodsFractional Riemman–Liouville operators-1Fractional Sobolev spaces-1Nonlocal problems-1https://purl.org/pe-repo/ocde/ford#1.01.02-1Fractional Sobolev space with Riemann–Liouville fractional derivative and application to a fractional concave–convex probleminfo:eu-repo/semantics/articlereponame:CONCYTEC-Institucionalinstname:Consejo Nacional de Ciencia Tecnología e Innovacióninstacron:CONCYTEC20.500.12390/3003oai:repositorio.concytec.gob.pe:20.500.12390/30032024-05-30 16:13:01.722http://purl.org/coar/access_right/c_14cbinfo:eu-repo/semantics/closedAccessmetadata only accesshttps://repositorio.concytec.gob.peRepositorio Institucional CONCYTECrepositorio@concytec.gob.pe#PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE#<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="2ce7ab3d-2b32-452c-82bd-4dcfd1f07df9"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Fractional Sobolev space with Riemann–Liouville fractional derivative and application to a fractional concave–convex problem</Title> <PublishedIn> <Publication> <Title>Advances in Operator Theory</Title> </Publication> </PublishedIn> <PublicationDate>2021</PublicationDate> <DOI>https://doi.org/10.1007/s43036-021-00159-w</DOI> <SCP-Number>2-s2.0-85112786087</SCP-Number> <Authors> <Author> <DisplayName>Ledesma C.E.T.</DisplayName> <Person id="rp08575" /> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> <Author> <DisplayName>Bonilla M.C.M.</DisplayName> <Person id="rp08576" /> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Birkhauser</DisplayName> <OrgUnit /> </Publisher> </Publishers> <Keyword>Variational methods</Keyword> <Keyword>Fractional Riemman–Liouville operators</Keyword> <Keyword>Fractional Sobolev spaces</Keyword> <Keyword>Nonlocal problems</Keyword> <Abstract>A new fractional function space EL?[a,b] with Riemann–Liouville fractional derivative and its related properties are established in this paper. Under this configuration, the following fractional concave–convex problem: xDb?(aDx?u)=?u?+up,in(a,b)B?(u)=0,in?(a,b)where ?? (0 , 1) , ?? (0 , 1) and p?(1,1+2?1-2?) if ??(0,12) and p? (1 , + ?) if ??(12,1). B?(u) represent the boundary condition of the problem which depend of the behavior of ?? (0 , 1) , that is: B?(u)={limx?a+aIx1-?u(x)=0,if??(0,12)u(a)=u(b)=0,if??(12,1).By using Ekeland’s variational principle and mountain pass theorem we show that the problem (0.1) at less has two nontrivial weak solutions. © 2021, Tusi Mathematical Research Group (TMRG).</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication> -1
dc.title.none.fl_str_mv Fractional Sobolev space with Riemann–Liouville fractional derivative and application to a fractional concave–convex problem
title Fractional Sobolev space with Riemann–Liouville fractional derivative and application to a fractional concave–convex problem
spellingShingle Fractional Sobolev space with Riemann–Liouville fractional derivative and application to a fractional concave–convex problem
Ledesma C.E.T.
Variational methods
Fractional Riemman–Liouville operators
Fractional Sobolev spaces
Nonlocal problems
https://purl.org/pe-repo/ocde/ford#1.01.02
title_short Fractional Sobolev space with Riemann–Liouville fractional derivative and application to a fractional concave–convex problem
title_full Fractional Sobolev space with Riemann–Liouville fractional derivative and application to a fractional concave–convex problem
title_fullStr Fractional Sobolev space with Riemann–Liouville fractional derivative and application to a fractional concave–convex problem
title_full_unstemmed Fractional Sobolev space with Riemann–Liouville fractional derivative and application to a fractional concave–convex problem
title_sort Fractional Sobolev space with Riemann–Liouville fractional derivative and application to a fractional concave–convex problem
author Ledesma C.E.T.
author_facet Ledesma C.E.T.
Bonilla M.C.M.
author_role author
author2 Bonilla M.C.M.
author2_role author
dc.contributor.author.fl_str_mv Ledesma C.E.T.
Bonilla M.C.M.
dc.subject.none.fl_str_mv Variational methods
topic Variational methods
Fractional Riemman–Liouville operators
Fractional Sobolev spaces
Nonlocal problems
https://purl.org/pe-repo/ocde/ford#1.01.02
dc.subject.es_PE.fl_str_mv Fractional Riemman–Liouville operators
Fractional Sobolev spaces
Nonlocal problems
dc.subject.ocde.none.fl_str_mv https://purl.org/pe-repo/ocde/ford#1.01.02
description This work was partially supported by CONCYTEC PERU, 379-2019-FONDECYT “ASPECTOS CUALITATIVOS DE ECUACIONES NO-LOCALES Y APLICACIONES”
publishDate 2021
dc.date.accessioned.none.fl_str_mv 2024-05-30T23:13:38Z
dc.date.available.none.fl_str_mv 2024-05-30T23:13:38Z
dc.date.issued.fl_str_mv 2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12390/3003
dc.identifier.doi.none.fl_str_mv https://doi.org/10.1007/s43036-021-00159-w
dc.identifier.scopus.none.fl_str_mv 2-s2.0-85112786087
url https://hdl.handle.net/20.500.12390/3003
https://doi.org/10.1007/s43036-021-00159-w
identifier_str_mv 2-s2.0-85112786087
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.ispartof.none.fl_str_mv Advances in Operator Theory
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Birkhauser
publisher.none.fl_str_mv Birkhauser
dc.source.none.fl_str_mv reponame:CONCYTEC-Institucional
instname:Consejo Nacional de Ciencia Tecnología e Innovación
instacron:CONCYTEC
instname_str Consejo Nacional de Ciencia Tecnología e Innovación
instacron_str CONCYTEC
institution CONCYTEC
reponame_str CONCYTEC-Institucional
collection CONCYTEC-Institucional
repository.name.fl_str_mv Repositorio Institucional CONCYTEC
repository.mail.fl_str_mv repositorio@concytec.gob.pe
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score 13.919034
Fractional Sobolev space with Riemann–Liouville fractional derivative and application to a fractional concave–convex problem
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