Periodic solutions for some fully nonlinear fourth order differential equations
Autor(a) principal: | |
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Data de Publicação: | 2011 |
Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10174/3701 |
Resumo: | In this paper we present sufficient conditions for the existence of periodic solutions to some nonlinear fourth order boundary value problems u(4)(x) = f(x; u(x); u′(x); u′′(x); u′′′(x)) u(i)(a) = u(i)(b); i = 0; 1; 2; 3; To the best of our knowledge it is the first time where this type of general nonlinearities is considered in fourth order equations with periodic boundary conditions. The difficulties in the odd derivatives are overcome due to the following arguments: the control on the third derivative is done by a Nagumo-type condition and the bounds on the first derivative are obtained by lower and upper solutions, not necessarily ordered. By this technique, not only it is proved the existence of a periodic solution, but also, some qualitative properties of the solution can be obtained. |
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7160 |
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Periodic solutions for some fully nonlinear fourth order differential equationsPeriodic solutionsFourth order nonlinear BVPIn this paper we present sufficient conditions for the existence of periodic solutions to some nonlinear fourth order boundary value problems u(4)(x) = f(x; u(x); u′(x); u′′(x); u′′′(x)) u(i)(a) = u(i)(b); i = 0; 1; 2; 3; To the best of our knowledge it is the first time where this type of general nonlinearities is considered in fourth order equations with periodic boundary conditions. The difficulties in the odd derivatives are overcome due to the following arguments: the control on the third derivative is done by a Nagumo-type condition and the bounds on the first derivative are obtained by lower and upper solutions, not necessarily ordered. By this technique, not only it is proved the existence of a periodic solution, but also, some qualitative properties of the solution can be obtained.2012-01-17T15:45:46Z2012-01-172011-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10174/3701http://hdl.handle.net/10174/3701porfminhos@uevora.pt334Minhós, Felizinfo: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:RCAAP2024-01-03T18:41:01Zoai:dspace.uevora.pt:10174/3701Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:59:05.342780Repositório 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 |
Periodic solutions for some fully nonlinear fourth order differential equations |
title |
Periodic solutions for some fully nonlinear fourth order differential equations |
spellingShingle |
Periodic solutions for some fully nonlinear fourth order differential equations Minhós, Feliz Periodic solutions Fourth order nonlinear BVP |
title_short |
Periodic solutions for some fully nonlinear fourth order differential equations |
title_full |
Periodic solutions for some fully nonlinear fourth order differential equations |
title_fullStr |
Periodic solutions for some fully nonlinear fourth order differential equations |
title_full_unstemmed |
Periodic solutions for some fully nonlinear fourth order differential equations |
title_sort |
Periodic solutions for some fully nonlinear fourth order differential equations |
author |
Minhós, Feliz |
author_facet |
Minhós, Feliz |
author_role |
author |
dc.contributor.author.fl_str_mv |
Minhós, Feliz |
dc.subject.por.fl_str_mv |
Periodic solutions Fourth order nonlinear BVP |
topic |
Periodic solutions Fourth order nonlinear BVP |
description |
In this paper we present sufficient conditions for the existence of periodic solutions to some nonlinear fourth order boundary value problems u(4)(x) = f(x; u(x); u′(x); u′′(x); u′′′(x)) u(i)(a) = u(i)(b); i = 0; 1; 2; 3; To the best of our knowledge it is the first time where this type of general nonlinearities is considered in fourth order equations with periodic boundary conditions. The difficulties in the odd derivatives are overcome due to the following arguments: the control on the third derivative is done by a Nagumo-type condition and the bounds on the first derivative are obtained by lower and upper solutions, not necessarily ordered. By this technique, not only it is proved the existence of a periodic solution, but also, some qualitative properties of the solution can be obtained. |
publishDate |
2011 |
dc.date.none.fl_str_mv |
2011-01-01T00:00:00Z 2012-01-17T15:45:46Z 2012-01-17 |
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/10174/3701 http://hdl.handle.net/10174/3701 |
url |
http://hdl.handle.net/10174/3701 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
fminhos@uevora.pt 334 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
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 |
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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 |
repository.mail.fl_str_mv |
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1799136473772982272 |