Homoclinic solution to zero of a non-autonomous, nonlinear, second order differential equation with quadratic growth on the derivative
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2022 |
| Tipo de documento: | Dissertação |
| Idioma: | eng |
| Título da fonte: | Repositório Institucional da UFJF |
| Texto Completo: | https://doi.org/10.34019/ufjf/di/2022/00039 https://repositorio.ufjf.br/jspui/handle/ufjf/14037 |
Resumo: | O objetivo principal deste trabalho é obter uma solução positiva, suave, par e homoclínica para o problema −(A(u)u 0 ) 0 (t) + u(t) = λa1(t)|u(t)| q−1 + |u(t)| p−1 + g(|u 0 (t)|), em R. Considerando 1 < q < 2 < p < +∞ e a1 ∈ L s (R) ∩ C(R), s = 2 2−q , uma função positiva e par. Também A : R → R uma função Lipschitz, suave (minímo C 1 (R)), não decrescente e satisfazendo ∃γ ∈ (0, 1) tal que 0 < γ ≤ A(t) ∀t ∈ R, e g : R → R uma função contínua satisfazendo 0 ≤ sg(s) ≤ |s| θ para todo s ∈ R, onde 2 < θ ≤ 3. Por homoclínica estamos nos referindo a “homoclínica para a origem” ou “homoclínica para zero”, isto é, a solução deve verificar limx→±∞ u(x) = 0. |
| id |
UFJF_e1c2dc432bf4af3a80419e985a4f30cf |
|---|---|
| oai_identifier_str |
oai:hermes.cpd.ufjf.br:ufjf/14037 |
| network_acronym_str |
UFJF |
| network_name_str |
Repositório Institucional da UFJF |
| repository_id_str |
|
| spelling |
Faria, Luiz Fernando de Oliveirahttp://lattes.cnpq.brFigueiredo, Giovany de Jesus Malcherhttp://lattes.cnpq.br/Toon, Eduardhttp://lattes.cnpq.br/http://lattes.cnpq.br/5895771157324473Corrêa Junior, Pablo dos Santos2022-05-05T13:30:53Z2022-05-052022-05-05T13:30:53Z2022-02-18https://doi.org/10.34019/ufjf/di/2022/00039https://repositorio.ufjf.br/jspui/handle/ufjf/14037O objetivo principal deste trabalho é obter uma solução positiva, suave, par e homoclínica para o problema −(A(u)u 0 ) 0 (t) + u(t) = λa1(t)|u(t)| q−1 + |u(t)| p−1 + g(|u 0 (t)|), em R. Considerando 1 < q < 2 < p < +∞ e a1 ∈ L s (R) ∩ C(R), s = 2 2−q , uma função positiva e par. Também A : R → R uma função Lipschitz, suave (minímo C 1 (R)), não decrescente e satisfazendo ∃γ ∈ (0, 1) tal que 0 < γ ≤ A(t) ∀t ∈ R, e g : R → R uma função contínua satisfazendo 0 ≤ sg(s) ≤ |s| θ para todo s ∈ R, onde 2 < θ ≤ 3. Por homoclínica estamos nos referindo a “homoclínica para a origem” ou “homoclínica para zero”, isto é, a solução deve verificar limx→±∞ u(x) = 0.The aim of this work is to obtain a positive, smooth, even and homoclinic solution to the problem −(A(u)u 0 ) 0 (t) + u(t) = λa1(t)|u(t)| q−1 + |u(t)| p−1 + g(|u 0 (t)|), in R. Considering 1 < q < 2 < p < +∞ and a1 ∈ L s (R) ∩ C(R), s = 2 2−q , a positive even function. Also A : R → R a Lipschitz, smooth (at least C 1 (R)), nondecreasing function satisfying ∃γ ∈ (0, 1) such that 0 < γ ≤ A(t) ∀t ∈ R, and g : R −→ R a continuous function satisfying 0 ≤ sg(s) ≤ |s| θ for all s ∈ R, where 2 < θ ≤ 3. By homoclinic we mean “homoclinic to the origin” or “homoclinic to zero” , i.e, the solution must verify limx→±∞ u(x) = 0.engUniversidade Federal de Juiz de Fora (UFJF)Mestrado Acadêmico em MatemáticaUFJFBrasilICE – Instituto de Ciências ExatasAttribution-ShareAlike 3.0 Brazilhttp://creativecommons.org/licenses/by-sa/3.0/br/info:eu-repo/semantics/openAccessCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAMétodo de GalerkinSolução homoclínicaCrescimento quadrático na derivadaEquação diferencialHomoclinic solution to zero of a non-autonomous, nonlinear, second order differential equation with quadratic growth on the derivativeinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisreponame:Repositório Institucional da UFJFinstname:Universidade Federal de Juiz de Fora (UFJF)instacron:UFJFORIGINALpablodossantoscorreajunior.pdfpablodossantoscorreajunior.pdfPDF/Aapplication/pdf913590https://repositorio.ufjf.br/jspui/bitstream/ufjf/14037/1/pablodossantoscorreajunior.pdfcb6bbf5e67f1ac0f211ca7d1e1cb5369MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-81031https://repositorio.ufjf.br/jspui/bitstream/ufjf/14037/2/license_rdf9b85e4235558a2887c2be3998124b615MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://repositorio.ufjf.br/jspui/bitstream/ufjf/14037/3/license.txt8a4605be74aa9ea9d79846c1fba20a33MD53TEXTpablodossantoscorreajunior.pdf.txtpablodossantoscorreajunior.pdf.txtExtracted texttext/plain65769https://repositorio.ufjf.br/jspui/bitstream/ufjf/14037/4/pablodossantoscorreajunior.pdf.txt382f90fb385a1ef93de1fce247c5806dMD54THUMBNAILpablodossantoscorreajunior.pdf.jpgpablodossantoscorreajunior.pdf.jpgGenerated Thumbnailimage/jpeg1175https://repositorio.ufjf.br/jspui/bitstream/ufjf/14037/5/pablodossantoscorreajunior.pdf.jpga9a48ab470aff26ffa6859840226af78MD55ufjf/140372022-11-18 12:41:55.229oai:hermes.cpd.ufjf.br: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Repositório InstitucionalPUBhttps://repositorio.ufjf.br/oai/requestopendoar:2022-11-18T14:41:55Repositório Institucional da UFJF - Universidade Federal de Juiz de Fora (UFJF)false |
| dc.title.pt_BR.fl_str_mv |
Homoclinic solution to zero of a non-autonomous, nonlinear, second order differential equation with quadratic growth on the derivative |
| title |
Homoclinic solution to zero of a non-autonomous, nonlinear, second order differential equation with quadratic growth on the derivative |
| spellingShingle |
Homoclinic solution to zero of a non-autonomous, nonlinear, second order differential equation with quadratic growth on the derivative Corrêa Junior, Pablo dos Santos CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA Método de Galerkin Solução homoclínica Crescimento quadrático na derivada Equação diferencial |
| title_short |
Homoclinic solution to zero of a non-autonomous, nonlinear, second order differential equation with quadratic growth on the derivative |
| title_full |
Homoclinic solution to zero of a non-autonomous, nonlinear, second order differential equation with quadratic growth on the derivative |
| title_fullStr |
Homoclinic solution to zero of a non-autonomous, nonlinear, second order differential equation with quadratic growth on the derivative |
| title_full_unstemmed |
Homoclinic solution to zero of a non-autonomous, nonlinear, second order differential equation with quadratic growth on the derivative |
| title_sort |
Homoclinic solution to zero of a non-autonomous, nonlinear, second order differential equation with quadratic growth on the derivative |
| author |
Corrêa Junior, Pablo dos Santos |
| author_facet |
Corrêa Junior, Pablo dos Santos |
| author_role |
author |
| dc.contributor.advisor1.fl_str_mv |
Faria, Luiz Fernando de Oliveira |
| dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br |
| dc.contributor.referee1.fl_str_mv |
Figueiredo, Giovany de Jesus Malcher |
| dc.contributor.referee1Lattes.fl_str_mv |
http://lattes.cnpq.br/ |
| dc.contributor.referee2.fl_str_mv |
Toon, Eduard |
| dc.contributor.referee2Lattes.fl_str_mv |
http://lattes.cnpq.br/ |
| dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/5895771157324473 |
| dc.contributor.author.fl_str_mv |
Corrêa Junior, Pablo dos Santos |
| contributor_str_mv |
Faria, Luiz Fernando de Oliveira Figueiredo, Giovany de Jesus Malcher Toon, Eduard |
| dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| topic |
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA Método de Galerkin Solução homoclínica Crescimento quadrático na derivada Equação diferencial |
| dc.subject.por.fl_str_mv |
Método de Galerkin Solução homoclínica Crescimento quadrático na derivada Equação diferencial |
| description |
O objetivo principal deste trabalho é obter uma solução positiva, suave, par e homoclínica para o problema −(A(u)u 0 ) 0 (t) + u(t) = λa1(t)|u(t)| q−1 + |u(t)| p−1 + g(|u 0 (t)|), em R. Considerando 1 < q < 2 < p < +∞ e a1 ∈ L s (R) ∩ C(R), s = 2 2−q , uma função positiva e par. Também A : R → R uma função Lipschitz, suave (minímo C 1 (R)), não decrescente e satisfazendo ∃γ ∈ (0, 1) tal que 0 < γ ≤ A(t) ∀t ∈ R, e g : R → R uma função contínua satisfazendo 0 ≤ sg(s) ≤ |s| θ para todo s ∈ R, onde 2 < θ ≤ 3. Por homoclínica estamos nos referindo a “homoclínica para a origem” ou “homoclínica para zero”, isto é, a solução deve verificar limx→±∞ u(x) = 0. |
| publishDate |
2022 |
| dc.date.accessioned.fl_str_mv |
2022-05-05T13:30:53Z |
| dc.date.available.fl_str_mv |
2022-05-05 2022-05-05T13:30:53Z |
| dc.date.issued.fl_str_mv |
2022-02-18 |
| 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 |
https://repositorio.ufjf.br/jspui/handle/ufjf/14037 |
| dc.identifier.doi.none.fl_str_mv |
https://doi.org/10.34019/ufjf/di/2022/00039 |
| url |
https://doi.org/10.34019/ufjf/di/2022/00039 https://repositorio.ufjf.br/jspui/handle/ufjf/14037 |
| dc.language.iso.fl_str_mv |
eng |
| language |
eng |
| dc.rights.driver.fl_str_mv |
Attribution-ShareAlike 3.0 Brazil http://creativecommons.org/licenses/by-sa/3.0/br/ info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
Attribution-ShareAlike 3.0 Brazil http://creativecommons.org/licenses/by-sa/3.0/br/ |
| eu_rights_str_mv |
openAccess |
| dc.publisher.none.fl_str_mv |
Universidade Federal de Juiz de Fora (UFJF) |
| dc.publisher.program.fl_str_mv |
Mestrado Acadêmico em Matemática |
| dc.publisher.initials.fl_str_mv |
UFJF |
| dc.publisher.country.fl_str_mv |
Brasil |
| dc.publisher.department.fl_str_mv |
ICE – Instituto de Ciências Exatas |
| publisher.none.fl_str_mv |
Universidade Federal de Juiz de Fora (UFJF) |
| dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFJF instname:Universidade Federal de Juiz de Fora (UFJF) instacron:UFJF |
| instname_str |
Universidade Federal de Juiz de Fora (UFJF) |
| instacron_str |
UFJF |
| institution |
UFJF |
| reponame_str |
Repositório Institucional da UFJF |
| collection |
Repositório Institucional da UFJF |
| bitstream.url.fl_str_mv |
https://repositorio.ufjf.br/jspui/bitstream/ufjf/14037/1/pablodossantoscorreajunior.pdf https://repositorio.ufjf.br/jspui/bitstream/ufjf/14037/2/license_rdf https://repositorio.ufjf.br/jspui/bitstream/ufjf/14037/3/license.txt https://repositorio.ufjf.br/jspui/bitstream/ufjf/14037/4/pablodossantoscorreajunior.pdf.txt https://repositorio.ufjf.br/jspui/bitstream/ufjf/14037/5/pablodossantoscorreajunior.pdf.jpg |
| bitstream.checksum.fl_str_mv |
cb6bbf5e67f1ac0f211ca7d1e1cb5369 9b85e4235558a2887c2be3998124b615 8a4605be74aa9ea9d79846c1fba20a33 382f90fb385a1ef93de1fce247c5806d a9a48ab470aff26ffa6859840226af78 |
| bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 |
| repository.name.fl_str_mv |
Repositório Institucional da UFJF - Universidade Federal de Juiz de Fora (UFJF) |
| repository.mail.fl_str_mv |
|
| _version_ |
1801661322978394112 |