Multiple solutions for a problem with resonance involving the p-Laplacian

Detalhes bibliográficos
Autor(a) principal: Alves, C. O.
Data de Publicação: 1998
Outros Autores: Carrião, P. C., Miyagaki, O. H.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: LOCUS Repositório Institucional da UFV
Texto Completo: http://dx.doi.org/10.1155/S1085337598000517
http://www.locus.ufv.br/handle/123456789/17244
Resumo: In this paper we will investigate the existence of multiple solutions for the problem (P)                                                −Δpu+g(x,u)=λ1h(x)|u|p−2u,     in     Ω,    u∈H01,p(Ω) where Δpu=div(|∇u|p−2∇u) is the p-Laplacian operator, Ω⫅ℝN is a bounded domain with smooth boundary, h and g are bounded functions, N≥1 and 1<p<∞. Using the Mountain Pass Theorem and the Ekeland Variational Principle, we will show the existence of at least three solutions for (P).
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spelling Alves, C. O.Carrião, P. C.Miyagaki, O. H.2018-02-05T12:34:58Z2018-02-05T12:34:58Z1998-03-181687-0409http://dx.doi.org/10.1155/S1085337598000517http://www.locus.ufv.br/handle/123456789/17244In this paper we will investigate the existence of multiple solutions for the problem (P)                                                −Δpu+g(x,u)=λ1h(x)|u|p−2u,     in     Ω,    u∈H01,p(Ω) where Δpu=div(|∇u|p−2∇u) is the p-Laplacian operator, Ω⫅ℝN is a bounded domain with smooth boundary, h and g are bounded functions, N≥1 and 1<p<∞. Using the Mountain Pass Theorem and the Ekeland Variational Principle, we will show the existence of at least three solutions for (P).engAbstract and Applied Analysisv. 3, n. 1-2, p. 191-201, 1998Multiple solutionsp-LaplacianMultiple solutions for a problem with resonance involving the p-Laplacianinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfinfo:eu-repo/semantics/openAccessreponame:LOCUS Repositório Institucional da UFVinstname:Universidade Federal de Viçosa (UFV)instacron:UFVORIGINALartigo.pdfartigo.pdftexto completoapplication/pdf1956067https://locus.ufv.br//bitstream/123456789/17244/1/artigo.pdf901e09d2a46b5c2076e6fc20eae1d6e1MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://locus.ufv.br//bitstream/123456789/17244/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52THUMBNAILartigo.pdf.jpgartigo.pdf.jpgIM Thumbnailimage/jpeg1251https://locus.ufv.br//bitstream/123456789/17244/3/artigo.pdf.jpg336cd4f0398ceb6bed8168a9cd2bb29eMD53123456789/172442018-02-05 22:01:06.914oai:locus.ufv.br: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Repositório InstitucionalPUBhttps://www.locus.ufv.br/oai/requestfabiojreis@ufv.bropendoar:21452018-02-06T01:01:06LOCUS Repositório Institucional da UFV - Universidade Federal de Viçosa (UFV)false
dc.title.en.fl_str_mv Multiple solutions for a problem with resonance involving the p-Laplacian
title Multiple solutions for a problem with resonance involving the p-Laplacian
spellingShingle Multiple solutions for a problem with resonance involving the p-Laplacian
Alves, C. O.
Multiple solutions
p-Laplacian
title_short Multiple solutions for a problem with resonance involving the p-Laplacian
title_full Multiple solutions for a problem with resonance involving the p-Laplacian
title_fullStr Multiple solutions for a problem with resonance involving the p-Laplacian
title_full_unstemmed Multiple solutions for a problem with resonance involving the p-Laplacian
title_sort Multiple solutions for a problem with resonance involving the p-Laplacian
author Alves, C. O.
author_facet Alves, C. O.
Carrião, P. C.
Miyagaki, O. H.
author_role author
author2 Carrião, P. C.
Miyagaki, O. H.
author2_role author
author
dc.contributor.author.fl_str_mv Alves, C. O.
Carrião, P. C.
Miyagaki, O. H.
dc.subject.pt-BR.fl_str_mv Multiple solutions
p-Laplacian
topic Multiple solutions
p-Laplacian
description In this paper we will investigate the existence of multiple solutions for the problem (P)                                                −Δpu+g(x,u)=λ1h(x)|u|p−2u,     in     Ω,    u∈H01,p(Ω) where Δpu=div(|∇u|p−2∇u) is the p-Laplacian operator, Ω⫅ℝN is a bounded domain with smooth boundary, h and g are bounded functions, N≥1 and 1<p<∞. Using the Mountain Pass Theorem and the Ekeland Variational Principle, we will show the existence of at least three solutions for (P).
publishDate 1998
dc.date.issued.fl_str_mv 1998-03-18
dc.date.accessioned.fl_str_mv 2018-02-05T12:34:58Z
dc.date.available.fl_str_mv 2018-02-05T12:34:58Z
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://dx.doi.org/10.1155/S1085337598000517
http://www.locus.ufv.br/handle/123456789/17244
dc.identifier.issn.none.fl_str_mv 1687-0409
identifier_str_mv 1687-0409
url http://dx.doi.org/10.1155/S1085337598000517
http://www.locus.ufv.br/handle/123456789/17244
dc.language.iso.fl_str_mv eng
language eng
dc.relation.ispartofseries.pt-BR.fl_str_mv v. 3, n. 1-2, p. 191-201, 1998
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 Abstract and Applied Analysis
publisher.none.fl_str_mv Abstract and Applied Analysis
dc.source.none.fl_str_mv reponame:LOCUS Repositório Institucional da UFV
instname:Universidade Federal de Viçosa (UFV)
instacron:UFV
instname_str Universidade Federal de Viçosa (UFV)
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reponame_str LOCUS Repositório Institucional da UFV
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