Solvability for a third order discontinuous fully equation with nonlinear functional boundary conditions

Detalhes bibliográficos
Autor(a) principal: Santos, Ana I.
Data de Publicação: 2006
Outros Autores: Cabada, Alberto, Minhós, Feliz M.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10174/2715
Resumo: We prove an existence and location result for the third order functional nonlinear boundary value problem u′′′(t) = f(t,u,u′(t),u′′(t)), for t∈[a,b], 0 = L₀(u,u′,u(t₀)), 0 = L₁(u,u′,u′(a),u′′(a)), 0 = L₂(u,u′,u′(b),u′′(b)), with t₀∈[a,b] given, f:I×C(I)×R²→R is a L¹- Carathéodory function allowing some discontinuities on t and L₀,L₁, L₂ are continuous functions depending functionally on u and u′. The arguments make use of an a priori estimate on u′′, lower and upper solutions method and degree theory. Applications to a multipoint problem and to a beam equation will be presented.
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spelling Solvability for a third order discontinuous fully equation with nonlinear functional boundary conditionsthird order functional problemsNagumo-type conditionLower and upper solutionsdegree theoryWe prove an existence and location result for the third order functional nonlinear boundary value problem u′′′(t) = f(t,u,u′(t),u′′(t)), for t∈[a,b], 0 = L₀(u,u′,u(t₀)), 0 = L₁(u,u′,u′(a),u′′(a)), 0 = L₂(u,u′,u′(b),u′′(b)), with t₀∈[a,b] given, f:I×C(I)×R²→R is a L¹- Carathéodory function allowing some discontinuities on t and L₀,L₁, L₂ are continuous functions depending functionally on u and u′. The arguments make use of an a priori estimate on u′′, lower and upper solutions method and degree theory. Applications to a multipoint problem and to a beam equation will be presented.Elsevier2011-06-30T09:46:00Z2011-06-302006-10-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article176394 bytesapplication/pdfhttp://hdl.handle.net/10174/2715http://hdl.handle.net/10174/2715engpag 735-7480022-247XVolume 322Journal of Mathematical Analysis and Applications2MAT -aims@uevora.ptcabada@usc.esfminhos@uevora.ptJournal of Mathematical Analysis and Applications334Santos, Ana I.Cabada, AlbertoMinhós, Feliz M.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-03T18:39:18Zoai:dspace.uevora.pt:10174/2715Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:58:19.414162Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Solvability for a third order discontinuous fully equation with nonlinear functional boundary conditions
title Solvability for a third order discontinuous fully equation with nonlinear functional boundary conditions
spellingShingle Solvability for a third order discontinuous fully equation with nonlinear functional boundary conditions
Santos, Ana I.
third order functional problems
Nagumo-type condition
Lower and upper solutions
degree theory
title_short Solvability for a third order discontinuous fully equation with nonlinear functional boundary conditions
title_full Solvability for a third order discontinuous fully equation with nonlinear functional boundary conditions
title_fullStr Solvability for a third order discontinuous fully equation with nonlinear functional boundary conditions
title_full_unstemmed Solvability for a third order discontinuous fully equation with nonlinear functional boundary conditions
title_sort Solvability for a third order discontinuous fully equation with nonlinear functional boundary conditions
author Santos, Ana I.
author_facet Santos, Ana I.
Cabada, Alberto
Minhós, Feliz M.
author_role author
author2 Cabada, Alberto
Minhós, Feliz M.
author2_role author
author
dc.contributor.author.fl_str_mv Santos, Ana I.
Cabada, Alberto
Minhós, Feliz M.
dc.subject.por.fl_str_mv third order functional problems
Nagumo-type condition
Lower and upper solutions
degree theory
topic third order functional problems
Nagumo-type condition
Lower and upper solutions
degree theory
description We prove an existence and location result for the third order functional nonlinear boundary value problem u′′′(t) = f(t,u,u′(t),u′′(t)), for t∈[a,b], 0 = L₀(u,u′,u(t₀)), 0 = L₁(u,u′,u′(a),u′′(a)), 0 = L₂(u,u′,u′(b),u′′(b)), with t₀∈[a,b] given, f:I×C(I)×R²→R is a L¹- Carathéodory function allowing some discontinuities on t and L₀,L₁, L₂ are continuous functions depending functionally on u and u′. The arguments make use of an a priori estimate on u′′, lower and upper solutions method and degree theory. Applications to a multipoint problem and to a beam equation will be presented.
publishDate 2006
dc.date.none.fl_str_mv 2006-10-01T00:00:00Z
2011-06-30T09:46:00Z
2011-06-30
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10174/2715
http://hdl.handle.net/10174/2715
url http://hdl.handle.net/10174/2715
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv pag 735-748
0022-247X
Volume 322
Journal of Mathematical Analysis and Applications
2
MAT -
aims@uevora.pt
cabada@usc.es
fminhos@uevora.pt
Journal of Mathematical Analysis and Applications
334
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 176394 bytes
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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