Homoclinic solutions for fractional Hamiltonian systems via variational method

We study the multiplicity of weak nonzero solutions for fractional Hamiltonian systems of the form $$_{t}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha} u(t)) +L(t)u(t)=a(t)\nabla V(t,u(t)),\quad t\in \mathbb{R},$$ where $\alpha\in (1/2,1]$, $_{-\infty}D_{t}^{\alpha}$ and $_{t}D_{\infty}^{\alpha}$ are...

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Detalles Bibliográficos
Autores: Cabada Fernández, Alberto, Tersian, Stepan
Tipo de recurso: capítulo de libro
Fecha de publicación:2019
País:España
Institución:Universidad de Santiago de Compostela (USC)
Repositorio:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Idioma:inglés
OAI Identifier:oai:minerva.usc.gal:10347/45450
Acceso en línea:https://hdl.handle.net/10347/45450
Access Level:acceso abierto
Palabra clave:Variational methods
Homoclinic solutions
1202 Análisis y análisis funcional
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spelling Homoclinic solutions for fractional Hamiltonian systems via variational methodCabada Fernández, AlbertoTersian, StepanVariational methodsHomoclinic solutions1202 Análisis y análisis funcionalWe study the multiplicity of weak nonzero solutions for fractional Hamiltonian systems of the form $$_{t}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha} u(t)) +L(t)u(t)=a(t)\nabla V(t,u(t)),\quad t\in \mathbb{R},$$ where $\alpha\in (1/2,1]$, $_{-\infty}D_{t}^{\alpha}$ and $_{t}D_{\infty}^{\alpha}$ are left and the right Liouville-Weyl fractional derivatives of order $\alpha$ on real line $\mathbb{R}$, $L(t)$ is a positive defined symmetric $n\times n$ matrix and $V:\mathbb{R}\times \mathbb{R}^n\to \mathbb{R}$ satisfies specific growth conditions. A result is proved using variational method and the generalized Clark's theorem. Some recent results are extended and improved.AIP PublishingUniversidade de Santiago de Compostela. Departamento de Análise Matemática20192019-11-1320192019-11-13book parthttp://purl.org/coar/resource_type/c_3248AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/bookPartapplication/pdfhttps://hdl.handle.net/10347/45450reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostelainstname:Universidad de Santiago de Compostela (USC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:minerva.usc.gal:10347/454502026-06-15T12:47:27Z
dc.title.none.fl_str_mv Homoclinic solutions for fractional Hamiltonian systems via variational method
title Homoclinic solutions for fractional Hamiltonian systems via variational method
spellingShingle Homoclinic solutions for fractional Hamiltonian systems via variational method
Cabada Fernández, Alberto
Variational methods
Homoclinic solutions
1202 Análisis y análisis funcional
title_short Homoclinic solutions for fractional Hamiltonian systems via variational method
title_full Homoclinic solutions for fractional Hamiltonian systems via variational method
title_fullStr Homoclinic solutions for fractional Hamiltonian systems via variational method
title_full_unstemmed Homoclinic solutions for fractional Hamiltonian systems via variational method
title_sort Homoclinic solutions for fractional Hamiltonian systems via variational method
dc.creator.none.fl_str_mv Cabada Fernández, Alberto
Tersian, Stepan
author Cabada Fernández, Alberto
author_facet Cabada Fernández, Alberto
Tersian, Stepan
author_role author
author2 Tersian, Stepan
author2_role author
dc.contributor.none.fl_str_mv Universidade de Santiago de Compostela. Departamento de Análise Matemática
dc.subject.none.fl_str_mv Variational methods
Homoclinic solutions
1202 Análisis y análisis funcional
topic Variational methods
Homoclinic solutions
1202 Análisis y análisis funcional
description We study the multiplicity of weak nonzero solutions for fractional Hamiltonian systems of the form $$_{t}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha} u(t)) +L(t)u(t)=a(t)\nabla V(t,u(t)),\quad t\in \mathbb{R},$$ where $\alpha\in (1/2,1]$, $_{-\infty}D_{t}^{\alpha}$ and $_{t}D_{\infty}^{\alpha}$ are left and the right Liouville-Weyl fractional derivatives of order $\alpha$ on real line $\mathbb{R}$, $L(t)$ is a positive defined symmetric $n\times n$ matrix and $V:\mathbb{R}\times \mathbb{R}^n\to \mathbb{R}$ satisfies specific growth conditions. A result is proved using variational method and the generalized Clark's theorem. Some recent results are extended and improved.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-11-13
2019
2019-11-13
dc.type.none.fl_str_mv book part
http://purl.org/coar/resource_type/c_3248
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
dc.identifier.none.fl_str_mv https://hdl.handle.net/10347/45450
url https://hdl.handle.net/10347/45450
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv AIP Publishing
publisher.none.fl_str_mv AIP Publishing
dc.source.none.fl_str_mv reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
instname:Universidad de Santiago de Compostela (USC)
instname_str Universidad de Santiago de Compostela (USC)
reponame_str Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
collection Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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