Non-autonomous perturbations for a class of quasilinear elliptic equations on R

Detalhes bibliográficos
Autor(a) principal: Miyagaki, O. H.
Data de Publicação: 2008
Outros Autores: Alves, M. J., Carrião, P. C.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: LOCUS Repositório Institucional da UFV
Texto Completo: https://doi.org/10.1016/j.jmaa.2008.02.055
http://www.locus.ufv.br/handle/123456789/22389
Resumo: This paper is concerned with the existence of two positive solutions for a class of quasilinear elliptic equations on R involving the p-Laplacian, with a non-autonomous perturbation. The first solution is obtained as a local minimum in a neighborhood of 0 and the second one by a mountain-pass argument. The special features of the problem here is the “complex” structure of the linear part which, in particular, oblige to work into the space W 1,p (R). Then one faces problems in the convergence of the sequences of derivatives un → u.
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spelling Miyagaki, O. H.Alves, M. J.Carrião, P. C.2018-10-23T17:59:27Z2018-10-23T17:59:27Z2008-08-010022247Xhttps://doi.org/10.1016/j.jmaa.2008.02.055http://www.locus.ufv.br/handle/123456789/22389This paper is concerned with the existence of two positive solutions for a class of quasilinear elliptic equations on R involving the p-Laplacian, with a non-autonomous perturbation. The first solution is obtained as a local minimum in a neighborhood of 0 and the second one by a mountain-pass argument. The special features of the problem here is the “complex” structure of the linear part which, in particular, oblige to work into the space W 1,p (R). Then one faces problems in the convergence of the sequences of derivatives un → u.engJournal of Mathematical Analysis and Applicationsv. 344, n. 1, p. 186-203, ago. 2008Non-autonomous perturbationsSchrödinger equationp-LaplacianVariational methodNon-autonomous perturbations for a class of quasilinear elliptic equations on Rinfo: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/pdf222535https://locus.ufv.br//bitstream/123456789/22389/1/artigo.pdf8b30c91ad40e4210c79a4b5af3afa282MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://locus.ufv.br//bitstream/123456789/22389/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52123456789/223892018-10-23 15:02:00.615oai:locus.ufv.br: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Repositório InstitucionalPUBhttps://www.locus.ufv.br/oai/requestfabiojreis@ufv.bropendoar:21452018-10-23T18:02LOCUS Repositório Institucional da UFV - Universidade Federal de Viçosa (UFV)false
dc.title.en.fl_str_mv Non-autonomous perturbations for a class of quasilinear elliptic equations on R
title Non-autonomous perturbations for a class of quasilinear elliptic equations on R
spellingShingle Non-autonomous perturbations for a class of quasilinear elliptic equations on R
Miyagaki, O. H.
Non-autonomous perturbations
Schrödinger equation
p-Laplacian
Variational method
title_short Non-autonomous perturbations for a class of quasilinear elliptic equations on R
title_full Non-autonomous perturbations for a class of quasilinear elliptic equations on R
title_fullStr Non-autonomous perturbations for a class of quasilinear elliptic equations on R
title_full_unstemmed Non-autonomous perturbations for a class of quasilinear elliptic equations on R
title_sort Non-autonomous perturbations for a class of quasilinear elliptic equations on R
author Miyagaki, O. H.
author_facet Miyagaki, O. H.
Alves, M. J.
Carrião, P. C.
author_role author
author2 Alves, M. J.
Carrião, P. C.
author2_role author
author
dc.contributor.author.fl_str_mv Miyagaki, O. H.
Alves, M. J.
Carrião, P. C.
dc.subject.pt-BR.fl_str_mv Non-autonomous perturbations
Schrödinger equation
p-Laplacian
Variational method
topic Non-autonomous perturbations
Schrödinger equation
p-Laplacian
Variational method
description This paper is concerned with the existence of two positive solutions for a class of quasilinear elliptic equations on R involving the p-Laplacian, with a non-autonomous perturbation. The first solution is obtained as a local minimum in a neighborhood of 0 and the second one by a mountain-pass argument. The special features of the problem here is the “complex” structure of the linear part which, in particular, oblige to work into the space W 1,p (R). Then one faces problems in the convergence of the sequences of derivatives un → u.
publishDate 2008
dc.date.issued.fl_str_mv 2008-08-01
dc.date.accessioned.fl_str_mv 2018-10-23T17:59:27Z
dc.date.available.fl_str_mv 2018-10-23T17:59:27Z
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 https://doi.org/10.1016/j.jmaa.2008.02.055
http://www.locus.ufv.br/handle/123456789/22389
dc.identifier.issn.none.fl_str_mv 0022247X
identifier_str_mv 0022247X
url https://doi.org/10.1016/j.jmaa.2008.02.055
http://www.locus.ufv.br/handle/123456789/22389
dc.language.iso.fl_str_mv eng
language eng
dc.relation.ispartofseries.pt-BR.fl_str_mv v. 344, n. 1, p. 186-203, ago. 2008
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 Journal of Mathematical Analysis and Applications
publisher.none.fl_str_mv Journal of Mathematical Analysis and Applications
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)
instacron_str UFV
institution UFV
reponame_str LOCUS Repositório Institucional da UFV
collection LOCUS Repositório Institucional da UFV
bitstream.url.fl_str_mv https://locus.ufv.br//bitstream/123456789/22389/1/artigo.pdf
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