Constant sign and nodal solutions for nonlinear elliptic equations with combined nonlinearities

Detalhes bibliográficos
Autor(a) principal: Aizicovici, S.
Data de Publicação: 2015
Outros Autores: Papageorgiou, N. S., Staicu, V.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/14988
Resumo: We study a parametric nonlinear Dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which is ”concave” (i.e., (p − 1)− sublinear) near zero and ”convex” (i.e., (p − 1)− superlinear) near ±1. Using variational methods combined with truncation and comparison techniques, we show that for all small values of the parameter > 0, the problem has at least five nontrivial smooth solutions (four of constant sign and the fifth nodal). In the Hilbert space case (p = 2), using Morse theory, we produce a sixth nontrivial smooth solution but we do not determine its sign.
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spelling Constant sign and nodal solutions for nonlinear elliptic equations with combined nonlinearitiesNodal solutionsNonlinear regularityLocal minimizerExtremal solutionsCritical groupsSuperlinear reactionConcave termWe study a parametric nonlinear Dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which is ”concave” (i.e., (p − 1)− sublinear) near zero and ”convex” (i.e., (p − 1)− superlinear) near ±1. Using variational methods combined with truncation and comparison techniques, we show that for all small values of the parameter > 0, the problem has at least five nontrivial smooth solutions (four of constant sign and the fifth nodal). In the Hilbert space case (p = 2), using Morse theory, we produce a sixth nontrivial smooth solution but we do not determine its sign.International Press2016-01-06T15:54:06Z2015-06-01T00:00:00Z2015-06info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/14988eng1073-277210.4310/MAA.2015.v22.n2.a5Aizicovici, S.Papageorgiou, N. S.Staicu, V.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:RCAAP2024-02-22T11:27:33Zoai:ria.ua.pt:10773/14988Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:50:26.501950Repositório 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 Constant sign and nodal solutions for nonlinear elliptic equations with combined nonlinearities
title Constant sign and nodal solutions for nonlinear elliptic equations with combined nonlinearities
spellingShingle Constant sign and nodal solutions for nonlinear elliptic equations with combined nonlinearities
Aizicovici, S.
Nodal solutions
Nonlinear regularity
Local minimizer
Extremal solutions
Critical groups
Superlinear reaction
Concave term
title_short Constant sign and nodal solutions for nonlinear elliptic equations with combined nonlinearities
title_full Constant sign and nodal solutions for nonlinear elliptic equations with combined nonlinearities
title_fullStr Constant sign and nodal solutions for nonlinear elliptic equations with combined nonlinearities
title_full_unstemmed Constant sign and nodal solutions for nonlinear elliptic equations with combined nonlinearities
title_sort Constant sign and nodal solutions for nonlinear elliptic equations with combined nonlinearities
author Aizicovici, S.
author_facet Aizicovici, S.
Papageorgiou, N. S.
Staicu, V.
author_role author
author2 Papageorgiou, N. S.
Staicu, V.
author2_role author
author
dc.contributor.author.fl_str_mv Aizicovici, S.
Papageorgiou, N. S.
Staicu, V.
dc.subject.por.fl_str_mv Nodal solutions
Nonlinear regularity
Local minimizer
Extremal solutions
Critical groups
Superlinear reaction
Concave term
topic Nodal solutions
Nonlinear regularity
Local minimizer
Extremal solutions
Critical groups
Superlinear reaction
Concave term
description We study a parametric nonlinear Dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which is ”concave” (i.e., (p − 1)− sublinear) near zero and ”convex” (i.e., (p − 1)− superlinear) near ±1. Using variational methods combined with truncation and comparison techniques, we show that for all small values of the parameter > 0, the problem has at least five nontrivial smooth solutions (four of constant sign and the fifth nodal). In the Hilbert space case (p = 2), using Morse theory, we produce a sixth nontrivial smooth solution but we do not determine its sign.
publishDate 2015
dc.date.none.fl_str_mv 2015-06-01T00:00:00Z
2015-06
2016-01-06T15:54:06Z
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/10773/14988
url http://hdl.handle.net/10773/14988
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1073-2772
10.4310/MAA.2015.v22.n2.a5
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv International Press
publisher.none.fl_str_mv International Press
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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