Existência de soluções para um problema do tipo (p; q)-Laplaciano com perturbação

Detalhes bibliográficos
Autor(a) principal: Somavilla, Fernanda
Data de Publicação: 2015
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional Manancial UFSM
Texto Completo: http://repositorio.ufsm.br/handle/1/17497
Resumo: In this paper, considering _ RN (N > 2) a bounded smooth domain, using blow-up techniques and the Leray Schauder Topological Degree theory, we intend to ensure the existence of positive solutions for a problem involving the p-Laplacian operator. Moreover, we employ variational methods, such as the Mountain Pass Theorem, to establish a result of existence and multiplicity of solutions to the following problem with a perturbation term �����_pu ����� _qu = _u_ + (a(x) + ")ur where 1 < q 6 p < _ + 1 < r + 1 < p_ and the parameters _; " > 0. The function a(x) 2 C1;_() is continuous, nonnegative and it vanishes in a subdomain of .
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spelling 2019-07-18T20:18:51Z2019-07-18T20:18:51Z2015-08-10http://repositorio.ufsm.br/handle/1/17497In this paper, considering _ RN (N > 2) a bounded smooth domain, using blow-up techniques and the Leray Schauder Topological Degree theory, we intend to ensure the existence of positive solutions for a problem involving the p-Laplacian operator. Moreover, we employ variational methods, such as the Mountain Pass Theorem, to establish a result of existence and multiplicity of solutions to the following problem with a perturbation term �����_pu ����� _qu = _u_ + (a(x) + ")ur where 1 < q 6 p < _ + 1 < r + 1 < p_ and the parameters _; " > 0. The function a(x) 2 C1;_() is continuous, nonnegative and it vanishes in a subdomain of .Neste trabalho, considerando RN (N > 2) um domínio limitado suave, através de técnicas de blow-up e teoria do Grau Topológico de Leray Schauder, pretendemos garantir a existência de solução positiva para um problema envolvendo o operador p-Laplaciano. Além disso, empregamos métodos variacionais, como o Teorema do Passo da Montanha, a fim de estabelecer um resultado de existência e multiplicidade de soluções para o problema com perturbação pu qu = u + (a(x) + ")ur onde 1 < q 6 p < + 1 < r + 1 < p e os parâmetros ; " > 0. A função a(x) 2 C1; ( ) (0 < < 1) e contínua não negativa e se anula em um subdomínio de .Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESporUniversidade Federal de Santa MariaCentro de Ciências Naturais e ExatasPrograma de Pós-Graduação em MatemáticaUFSMBrasilMatemáticaAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccess(p; q)-LaplacianoExistência e multiplicidade de soluçõesMétodos variacionaisGrau topológico de Leray-Schauder(p; q)-LaplacianExistence and multiplicity of solutionsVarational methodsLeray-Schauder degreeCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAExistência de soluções para um problema do tipo (p; q)-Laplaciano com perturbaçãoExistence of solutions for a (p; q)-Laplacian type problem with perturbationinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisMiotto, Taísa Jungeshttp://lattes.cnpq.br/3442278498547366Miotto, Márcio Luíshttp://lattes.cnpq.br/4220318089537530Miyagaki, Olimpio Hiroshihttp://lattes.cnpq.br/2646698407526867Godoi, Juliano Damião Bittencourt dehttp://lattes.cnpq.br/7641553268884764http://lattes.cnpq.br/0280451137694299Somavilla, Fernanda100100000008600e7cf3d6e-5fab-4115-b82f-4bb25fee64005733949b-6731-4adc-a260-6d394d93c25c4128e0f4-9330-419e-9901-9a5a91b6251ba95f113d-97f7-4456-bb52-d60c39202b3c224504f8-b425-48f7-b738-55e731ca4e8dreponame:Repositório Institucional Manancial UFSMinstname:Universidade Federal de Santa Maria (UFSM)instacron:UFSMORIGINALDIS_PPGMATEMATICA_2015_SOMAVILLA_FERNANDA.pdfDIS_PPGMATEMATICA_2015_SOMAVILLA_FERNANDA.pdfDissertação de Mestradoapplication/pdf1459096http://repositorio.ufsm.br/bitstream/1/17497/1/DIS_PPGMATEMATICA_2015_SOMAVILLA_FERNANDA.pdf1130b049327fc363b9ecef38a3bd9abeMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.por.fl_str_mv Existência de soluções para um problema do tipo (p; q)-Laplaciano com perturbação
dc.title.alternative.eng.fl_str_mv Existence of solutions for a (p; q)-Laplacian type problem with perturbation
title Existência de soluções para um problema do tipo (p; q)-Laplaciano com perturbação
spellingShingle Existência de soluções para um problema do tipo (p; q)-Laplaciano com perturbação
Somavilla, Fernanda
(p; q)-Laplaciano
Existência e multiplicidade de soluções
Métodos variacionais
Grau topológico de Leray-Schauder
(p; q)-Laplacian
Existence and multiplicity of solutions
Varational methods
Leray-Schauder degree
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Existência de soluções para um problema do tipo (p; q)-Laplaciano com perturbação
title_full Existência de soluções para um problema do tipo (p; q)-Laplaciano com perturbação
title_fullStr Existência de soluções para um problema do tipo (p; q)-Laplaciano com perturbação
title_full_unstemmed Existência de soluções para um problema do tipo (p; q)-Laplaciano com perturbação
title_sort Existência de soluções para um problema do tipo (p; q)-Laplaciano com perturbação
author Somavilla, Fernanda
author_facet Somavilla, Fernanda
author_role author
dc.contributor.advisor1.fl_str_mv Miotto, Taísa Junges
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/3442278498547366
dc.contributor.advisor-co1.fl_str_mv Miotto, Márcio Luís
dc.contributor.advisor-co1Lattes.fl_str_mv http://lattes.cnpq.br/4220318089537530
dc.contributor.referee1.fl_str_mv Miyagaki, Olimpio Hiroshi
dc.contributor.referee1Lattes.fl_str_mv http://lattes.cnpq.br/2646698407526867
dc.contributor.referee2.fl_str_mv Godoi, Juliano Damião Bittencourt de
dc.contributor.referee2Lattes.fl_str_mv http://lattes.cnpq.br/7641553268884764
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/0280451137694299
dc.contributor.author.fl_str_mv Somavilla, Fernanda
contributor_str_mv Miotto, Taísa Junges
Miotto, Márcio Luís
Miyagaki, Olimpio Hiroshi
Godoi, Juliano Damião Bittencourt de
dc.subject.por.fl_str_mv (p; q)-Laplaciano
Existência e multiplicidade de soluções
Métodos variacionais
Grau topológico de Leray-Schauder
topic (p; q)-Laplaciano
Existência e multiplicidade de soluções
Métodos variacionais
Grau topológico de Leray-Schauder
(p; q)-Laplacian
Existence and multiplicity of solutions
Varational methods
Leray-Schauder degree
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv (p; q)-Laplacian
Existence and multiplicity of solutions
Varational methods
Leray-Schauder degree
dc.subject.cnpq.fl_str_mv CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
description In this paper, considering _ RN (N > 2) a bounded smooth domain, using blow-up techniques and the Leray Schauder Topological Degree theory, we intend to ensure the existence of positive solutions for a problem involving the p-Laplacian operator. Moreover, we employ variational methods, such as the Mountain Pass Theorem, to establish a result of existence and multiplicity of solutions to the following problem with a perturbation term �����_pu ����� _qu = _u_ + (a(x) + ")ur where 1 < q 6 p < _ + 1 < r + 1 < p_ and the parameters _; " > 0. The function a(x) 2 C1;_() is continuous, nonnegative and it vanishes in a subdomain of .
publishDate 2015
dc.date.issued.fl_str_mv 2015-08-10
dc.date.accessioned.fl_str_mv 2019-07-18T20:18:51Z
dc.date.available.fl_str_mv 2019-07-18T20:18:51Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://repositorio.ufsm.br/handle/1/17497
url http://repositorio.ufsm.br/handle/1/17497
dc.language.iso.fl_str_mv por
language por
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dc.rights.driver.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Federal de Santa Maria
Centro de Ciências Naturais e Exatas
dc.publisher.program.fl_str_mv Programa de Pós-Graduação em Matemática
dc.publisher.initials.fl_str_mv UFSM
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv Matemática
publisher.none.fl_str_mv Universidade Federal de Santa Maria
Centro de Ciências Naturais e Exatas
dc.source.none.fl_str_mv reponame:Repositório Institucional Manancial UFSM
instname:Universidade Federal de Santa Maria (UFSM)
instacron:UFSM
instname_str Universidade Federal de Santa Maria (UFSM)
instacron_str UFSM
institution UFSM
reponame_str Repositório Institucional Manancial UFSM
collection Repositório Institucional Manancial UFSM
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