Multiplicity of solutions for a class of nonlinear nonhomogeneous elliptic equations

Detalhes bibliográficos
Autor(a) principal: Aizicovici, S.
Data de Publicação: 2014
Outros Autores: Papageorgiou, N. S., Staicu, Vasile
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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spelling 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
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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
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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)
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