Positive solution for a class of coupled (p, q)-Laplacian nonlinear systems.
Autor(a) principal: | |
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Data de Publicação: | 2014 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFOP |
Texto Completo: | http://www.repositorio.ufop.br/handle/123456789/4786 https://doi.org/10.1186/1687-2770-2014-21 |
Resumo: | In this article, we prove the existence of a nontrivial positive solution for the elliptic system ⎧⎨ ⎩ –_pu = ω(x)f (v) in_, –_qv = ρ(x)g(u) in_, (u, v) = (0,0) on ∂_, where_p denotes the p-Laplacian operator, p, q > 1 and _ is a smooth bounded domain in RN (N ≥ 2). The weight functions ω and ρ are continuous, nonnegative and not identically null in _, and the nonlinearities f and g are continuous and satisfy simple hypotheses of local behavior, without involving monotonicity hypotheses or conditions at∞. We apply the fixed point theorem in a cone to obtain our result. MSC: 35B09; 35J47; 58J20 |
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Martins, Eder MarinhoFerreira, Wenderson Marques2015-03-25T16:10:59Z2015-03-25T16:10:59Z2014MARTINS, E. M.; FERREIRA, W. M. Positive solution for a class of coupled (p, q)-Laplacian nonlinear systems. Boundary Value Problems, v. 2014, p. 21, 2014. Disponível em: <http://www.boundaryvalueproblems.com/content/pdf/1687-2770-2014-21.pdf>. Acesso em: 06 mar. 2015.1687-2762http://www.repositorio.ufop.br/handle/123456789/4786https://doi.org/10.1186/1687-2770-2014-21In this article, we prove the existence of a nontrivial positive solution for the elliptic system ⎧⎨ ⎩ –_pu = ω(x)f (v) in_, –_qv = ρ(x)g(u) in_, (u, v) = (0,0) on ∂_, where_p denotes the p-Laplacian operator, p, q > 1 and _ is a smooth bounded domain in RN (N ≥ 2). The weight functions ω and ρ are continuous, nonnegative and not identically null in _, and the nonlinearities f and g are continuous and satisfy simple hypotheses of local behavior, without involving monotonicity hypotheses or conditions at∞. We apply the fixed point theorem in a cone to obtain our result. MSC: 35B09; 35J47; 58J20Positive solution for a class of coupled (p, q)-Laplacian nonlinear systems.info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleO periódico Boundary Value Problems permite o arquivamento da versão/PDF do editor no Repositório Institucional. Fonte: Sherpa/Romeo <http://www.sherpa.ac.uk/romeo/search.php?issn=1687-2762>. Acesso em: 20 out. 2016.info:eu-repo/semantics/openAccessengreponame:Repositório Institucional da UFOPinstname:Universidade Federal de Ouro Preto (UFOP)instacron:UFOPLICENSElicense.txtlicense.txttext/plain; charset=utf-82636http://www.repositorio.ufop.br/bitstream/123456789/4786/2/license.txtc2ffdd99e58acf69202dff00d361f23aMD52ORIGINALARTIGO_PositiveSolutionClass.pdfARTIGO_PositiveSolutionClass.pdfapplication/pdf637468http://www.repositorio.ufop.br/bitstream/123456789/4786/1/ARTIGO_PositiveSolutionClass.pdf2b5f211aaeabdeca6408f60909b33362MD51123456789/47862019-06-28 13:57:02.615oai:localhost: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Repositório InstitucionalPUBhttp://www.repositorio.ufop.br/oai/requestrepositorio@ufop.edu.bropendoar:32332019-06-28T17:57:02Repositório Institucional da UFOP - Universidade Federal de Ouro Preto (UFOP)false |
dc.title.pt_BR.fl_str_mv |
Positive solution for a class of coupled (p, q)-Laplacian nonlinear systems. |
title |
Positive solution for a class of coupled (p, q)-Laplacian nonlinear systems. |
spellingShingle |
Positive solution for a class of coupled (p, q)-Laplacian nonlinear systems. Martins, Eder Marinho |
title_short |
Positive solution for a class of coupled (p, q)-Laplacian nonlinear systems. |
title_full |
Positive solution for a class of coupled (p, q)-Laplacian nonlinear systems. |
title_fullStr |
Positive solution for a class of coupled (p, q)-Laplacian nonlinear systems. |
title_full_unstemmed |
Positive solution for a class of coupled (p, q)-Laplacian nonlinear systems. |
title_sort |
Positive solution for a class of coupled (p, q)-Laplacian nonlinear systems. |
author |
Martins, Eder Marinho |
author_facet |
Martins, Eder Marinho Ferreira, Wenderson Marques |
author_role |
author |
author2 |
Ferreira, Wenderson Marques |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Martins, Eder Marinho Ferreira, Wenderson Marques |
description |
In this article, we prove the existence of a nontrivial positive solution for the elliptic system ⎧⎨ ⎩ –_pu = ω(x)f (v) in_, –_qv = ρ(x)g(u) in_, (u, v) = (0,0) on ∂_, where_p denotes the p-Laplacian operator, p, q > 1 and _ is a smooth bounded domain in RN (N ≥ 2). The weight functions ω and ρ are continuous, nonnegative and not identically null in _, and the nonlinearities f and g are continuous and satisfy simple hypotheses of local behavior, without involving monotonicity hypotheses or conditions at∞. We apply the fixed point theorem in a cone to obtain our result. MSC: 35B09; 35J47; 58J20 |
publishDate |
2014 |
dc.date.issued.fl_str_mv |
2014 |
dc.date.accessioned.fl_str_mv |
2015-03-25T16:10:59Z |
dc.date.available.fl_str_mv |
2015-03-25T16:10:59Z |
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.citation.fl_str_mv |
MARTINS, E. M.; FERREIRA, W. M. Positive solution for a class of coupled (p, q)-Laplacian nonlinear systems. Boundary Value Problems, v. 2014, p. 21, 2014. Disponível em: <http://www.boundaryvalueproblems.com/content/pdf/1687-2770-2014-21.pdf>. Acesso em: 06 mar. 2015. |
dc.identifier.uri.fl_str_mv |
http://www.repositorio.ufop.br/handle/123456789/4786 |
dc.identifier.issn.none.fl_str_mv |
1687-2762 |
dc.identifier.doi.none.fl_str_mv |
https://doi.org/10.1186/1687-2770-2014-21 |
identifier_str_mv |
MARTINS, E. M.; FERREIRA, W. M. Positive solution for a class of coupled (p, q)-Laplacian nonlinear systems. Boundary Value Problems, v. 2014, p. 21, 2014. Disponível em: <http://www.boundaryvalueproblems.com/content/pdf/1687-2770-2014-21.pdf>. Acesso em: 06 mar. 2015. 1687-2762 |
url |
http://www.repositorio.ufop.br/handle/123456789/4786 https://doi.org/10.1186/1687-2770-2014-21 |
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eng |
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eng |
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UFOP |
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