Multiplicity of solutions for a class of nonlinear nonhomogeneous elliptic equations
Autor(a) principal: | |
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Data de Publicação: | 2014 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/18726 |
Resumo: | We consider nonlinear, nonhomogeneous Dirichlet problems driven by the sum of a p−Laplacian (p > 2) and a Laplacian, with a reaction term which has space dependent zeros of constant sign. We prove three muliplicity theorems for such equations providing precise sign information for all solutions. In the first multiplicity theorem, we do not impose any growth condition on the reaction near ±∞: In the other two, we assume that the reaction is (p − 1)− linear and resonant with respect to principal eigenvalue of ( −△p;W1,p 0 (Ω) ) : Our approach uses variational methods based on the critical point theory, together with suitable truncation and comparison techniques and Morse theory (critical groups). |
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Multiplicity of solutions for a class of nonlinear nonhomogeneous elliptic equationsConsant sign and nodal solutionsNonlinear regularityCritical goupsTruncation and comparison techniquesWe consider nonlinear, nonhomogeneous Dirichlet problems driven by the sum of a p−Laplacian (p > 2) and a Laplacian, with a reaction term which has space dependent zeros of constant sign. We prove three muliplicity theorems for such equations providing precise sign information for all solutions. In the first multiplicity theorem, we do not impose any growth condition on the reaction near ±∞: In the other two, we assume that the reaction is (p − 1)− linear and resonant with respect to principal eigenvalue of ( −△p;W1,p 0 (Ω) ) : Our approach uses variational methods based on the critical point theory, together with suitable truncation and comparison techniques and Morse theory (critical groups).Yokohama Publishers2017-11-07T11:18:08Z2014-01-01T00:00:00Z2014info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/18726eng1880-5221Aizicovici, S.Papageorgiou, N. S.Staicu, Vasileinfo: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:RCAAP2024-02-22T11:36:14Zoai:ria.ua.pt:10773/18726Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:53:38.368183Repositório 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 |
Multiplicity of solutions for a class of nonlinear nonhomogeneous elliptic equations |
title |
Multiplicity of solutions for a class of nonlinear nonhomogeneous elliptic equations |
spellingShingle |
Multiplicity of solutions for a class of nonlinear nonhomogeneous elliptic equations Aizicovici, S. Consant sign and nodal solutions Nonlinear regularity Critical goups Truncation and comparison techniques |
title_short |
Multiplicity of solutions for a class of nonlinear nonhomogeneous elliptic equations |
title_full |
Multiplicity of solutions for a class of nonlinear nonhomogeneous elliptic equations |
title_fullStr |
Multiplicity of solutions for a class of nonlinear nonhomogeneous elliptic equations |
title_full_unstemmed |
Multiplicity of solutions for a class of nonlinear nonhomogeneous elliptic equations |
title_sort |
Multiplicity of solutions for a class of nonlinear nonhomogeneous elliptic equations |
author |
Aizicovici, S. |
author_facet |
Aizicovici, S. Papageorgiou, N. S. Staicu, Vasile |
author_role |
author |
author2 |
Papageorgiou, N. S. Staicu, Vasile |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Aizicovici, S. Papageorgiou, N. S. Staicu, Vasile |
dc.subject.por.fl_str_mv |
Consant sign and nodal solutions Nonlinear regularity Critical goups Truncation and comparison techniques |
topic |
Consant sign and nodal solutions Nonlinear regularity Critical goups Truncation and comparison techniques |
description |
We consider nonlinear, nonhomogeneous Dirichlet problems driven by the sum of a p−Laplacian (p > 2) and a Laplacian, with a reaction term which has space dependent zeros of constant sign. We prove three muliplicity theorems for such equations providing precise sign information for all solutions. In the first multiplicity theorem, we do not impose any growth condition on the reaction near ±∞: In the other two, we assume that the reaction is (p − 1)− linear and resonant with respect to principal eigenvalue of ( −△p;W1,p 0 (Ω) ) : Our approach uses variational methods based on the critical point theory, together with suitable truncation and comparison techniques and Morse theory (critical groups). |
publishDate |
2014 |
dc.date.none.fl_str_mv |
2014-01-01T00:00:00Z 2014 2017-11-07T11:18:08Z |
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/10773/18726 |
url |
http://hdl.handle.net/10773/18726 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1880-5221 |
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 |
Yokohama Publishers |
publisher.none.fl_str_mv |
Yokohama Publishers |
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 |
repository.mail.fl_str_mv |
|
_version_ |
1799137587903856640 |