Soliton solutions for quasilinear Schrödinger equations with critical growth
Autor(a) principal: | |
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Data de Publicação: | 2010 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | LOCUS Repositório Institucional da UFV |
Texto Completo: | https://doi.org/10.1016/j.jde.2009.11.030 http://www.locus.ufv.br/handle/123456789/21947 |
Resumo: | In this paper we establish the existence of standing wave solutions for quasilinear Schrödinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration–compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9]. |
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Miyagaki, Olímpio H.Ó, João M. Bezerra doSoares, Sérgio H. M.2018-09-24T13:37:19Z2018-09-24T13:37:19Z2010-02-1500220396https://doi.org/10.1016/j.jde.2009.11.030http://www.locus.ufv.br/handle/123456789/21947In this paper we establish the existence of standing wave solutions for quasilinear Schrödinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration–compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9].engJournal of Differential Equationsv. 248, n. 4, p. 722- 744, fev. 2010Schrödinger equationsStanding wave solutionsVariational methodsMinimax methodsCritical exponentSoliton solutions for quasilinear Schrödinger equations with critical growthinfo: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/pdf276185https://locus.ufv.br//bitstream/123456789/21947/1/artigo.pdf83c5d08790b734ed678ff75b25ac27b9MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://locus.ufv.br//bitstream/123456789/21947/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52THUMBNAILartigo.pdf.jpgartigo.pdf.jpgIM Thumbnailimage/jpeg5037https://locus.ufv.br//bitstream/123456789/21947/3/artigo.pdf.jpg5580e380385b1655217f0c7deb4da2c1MD53123456789/219472018-09-24 23:00:37.154oai:locus.ufv.br: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Repositório InstitucionalPUBhttps://www.locus.ufv.br/oai/requestfabiojreis@ufv.bropendoar:21452018-09-25T02:00:37LOCUS Repositório Institucional da UFV - Universidade Federal de Viçosa (UFV)false |
dc.title.en.fl_str_mv |
Soliton solutions for quasilinear Schrödinger equations with critical growth |
title |
Soliton solutions for quasilinear Schrödinger equations with critical growth |
spellingShingle |
Soliton solutions for quasilinear Schrödinger equations with critical growth Miyagaki, Olímpio H. Schrödinger equations Standing wave solutions Variational methods Minimax methods Critical exponent |
title_short |
Soliton solutions for quasilinear Schrödinger equations with critical growth |
title_full |
Soliton solutions for quasilinear Schrödinger equations with critical growth |
title_fullStr |
Soliton solutions for quasilinear Schrödinger equations with critical growth |
title_full_unstemmed |
Soliton solutions for quasilinear Schrödinger equations with critical growth |
title_sort |
Soliton solutions for quasilinear Schrödinger equations with critical growth |
author |
Miyagaki, Olímpio H. |
author_facet |
Miyagaki, Olímpio H. Ó, João M. Bezerra do Soares, Sérgio H. M. |
author_role |
author |
author2 |
Ó, João M. Bezerra do Soares, Sérgio H. M. |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Miyagaki, Olímpio H. Ó, João M. Bezerra do Soares, Sérgio H. M. |
dc.subject.pt-BR.fl_str_mv |
Schrödinger equations Standing wave solutions Variational methods Minimax methods Critical exponent |
topic |
Schrödinger equations Standing wave solutions Variational methods Minimax methods Critical exponent |
description |
In this paper we establish the existence of standing wave solutions for quasilinear Schrödinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration–compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9]. |
publishDate |
2010 |
dc.date.issued.fl_str_mv |
2010-02-15 |
dc.date.accessioned.fl_str_mv |
2018-09-24T13:37:19Z |
dc.date.available.fl_str_mv |
2018-09-24T13:37:19Z |
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.jde.2009.11.030 http://www.locus.ufv.br/handle/123456789/21947 |
dc.identifier.issn.none.fl_str_mv |
00220396 |
identifier_str_mv |
00220396 |
url |
https://doi.org/10.1016/j.jde.2009.11.030 http://www.locus.ufv.br/handle/123456789/21947 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartofseries.pt-BR.fl_str_mv |
v. 248, n. 4, p. 722- 744, fev. 2010 |
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 Differential Equations |
publisher.none.fl_str_mv |
Journal of Differential Equations |
dc.source.none.fl_str_mv |
reponame:LOCUS Repositório Institucional da UFV instname:Universidade Federal de Viçosa (UFV) instacron:UFV |
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Universidade Federal de Viçosa (UFV) |
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UFV |
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LOCUS Repositório Institucional da UFV |
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LOCUS Repositório Institucional da UFV |
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