Energy dependent potential problems for the one dimensional p-Laplacian operator

Autores
Koyunbakan, Hikmet; Pinasco, Juan Pablo; Scarola, Cristian
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this work we analyze a nonlinear eigenvalue problem for the p-Laplacian operator with zero Dirichlet boundary conditions. We assume that the problem has a potential which depends on the eigenvalue parameter, and we show that, for n big enough, there exists a real eigenvalue λn, and their corresponding eigenfunctions have exactly n nodal domains. We characterize the asymptotic behavior of these eigenvalues, obtaining two terms in the asymptotic expansion of λn in powers of n. Finally, we study the inverse nodal problem in the case of energy dependent potentials, showing that some subset of the zeros of the corresponding eigenfunctions is enough to determine the main term of the potential.
Fil: Koyunbakan, Hikmet. Firat Universitesi; Turquía
Fil: Pinasco, Juan Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Scarola, Cristian. Universidad Nacional de la Pampa. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
ASYMPTOTIC BEHAVIOR
EIGENVALUES
NODAL INVERSE PROBLEM
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/116929
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Energy dependent potential problems for the one dimensional p-Laplacian operatorKoyunbakan, HikmetPinasco, Juan PabloScarola, CristianASYMPTOTIC BEHAVIOREIGENVALUESNODAL INVERSE PROBLEMhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this work we analyze a nonlinear eigenvalue problem for the p-Laplacian operator with zero Dirichlet boundary conditions. We assume that the problem has a potential which depends on the eigenvalue parameter, and we show that, for n big enough, there exists a real eigenvalue λn, and their corresponding eigenfunctions have exactly n nodal domains. We characterize the asymptotic behavior of these eigenvalues, obtaining two terms in the asymptotic expansion of λn in powers of n. Finally, we study the inverse nodal problem in the case of energy dependent potentials, showing that some subset of the zeros of the corresponding eigenfunctions is enough to determine the main term of the potential.Fil: Koyunbakan, Hikmet. Firat Universitesi; TurquíaFil: Pinasco, Juan Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Scarola, Cristian. Universidad Nacional de la Pampa. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaPergamon-Elsevier Science Ltd2019-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/116929Koyunbakan, Hikmet; Pinasco, Juan Pablo; Scarola, Cristian; Energy dependent potential problems for the one dimensional p-Laplacian operator; Pergamon-Elsevier Science Ltd; Nonlinear Analysis-real World Applications; 45; 2-2019; 285-2981468-1218CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.nonrwa.2018.07.001info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S1468121818305649info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:08:08Zoai:ri.conicet.gov.ar:11336/116929instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:08:08.657CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Energy dependent potential problems for the one dimensional p-Laplacian operator
title Energy dependent potential problems for the one dimensional p-Laplacian operator
spellingShingle Energy dependent potential problems for the one dimensional p-Laplacian operator
Koyunbakan, Hikmet
ASYMPTOTIC BEHAVIOR
EIGENVALUES
NODAL INVERSE PROBLEM
title_short Energy dependent potential problems for the one dimensional p-Laplacian operator
title_full Energy dependent potential problems for the one dimensional p-Laplacian operator
title_fullStr Energy dependent potential problems for the one dimensional p-Laplacian operator
title_full_unstemmed Energy dependent potential problems for the one dimensional p-Laplacian operator
title_sort Energy dependent potential problems for the one dimensional p-Laplacian operator
dc.creator.none.fl_str_mv Koyunbakan, Hikmet
Pinasco, Juan Pablo
Scarola, Cristian
author Koyunbakan, Hikmet
author_facet Koyunbakan, Hikmet
Pinasco, Juan Pablo
Scarola, Cristian
author_role author
author2 Pinasco, Juan Pablo
Scarola, Cristian
author2_role author
author
dc.subject.none.fl_str_mv ASYMPTOTIC BEHAVIOR
EIGENVALUES
NODAL INVERSE PROBLEM
topic ASYMPTOTIC BEHAVIOR
EIGENVALUES
NODAL INVERSE PROBLEM
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this work we analyze a nonlinear eigenvalue problem for the p-Laplacian operator with zero Dirichlet boundary conditions. We assume that the problem has a potential which depends on the eigenvalue parameter, and we show that, for n big enough, there exists a real eigenvalue λn, and their corresponding eigenfunctions have exactly n nodal domains. We characterize the asymptotic behavior of these eigenvalues, obtaining two terms in the asymptotic expansion of λn in powers of n. Finally, we study the inverse nodal problem in the case of energy dependent potentials, showing that some subset of the zeros of the corresponding eigenfunctions is enough to determine the main term of the potential.
Fil: Koyunbakan, Hikmet. Firat Universitesi; Turquía
Fil: Pinasco, Juan Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Scarola, Cristian. Universidad Nacional de la Pampa. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description In this work we analyze a nonlinear eigenvalue problem for the p-Laplacian operator with zero Dirichlet boundary conditions. We assume that the problem has a potential which depends on the eigenvalue parameter, and we show that, for n big enough, there exists a real eigenvalue λn, and their corresponding eigenfunctions have exactly n nodal domains. We characterize the asymptotic behavior of these eigenvalues, obtaining two terms in the asymptotic expansion of λn in powers of n. Finally, we study the inverse nodal problem in the case of energy dependent potentials, showing that some subset of the zeros of the corresponding eigenfunctions is enough to determine the main term of the potential.
publishDate 2019
dc.date.none.fl_str_mv 2019-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/116929
Koyunbakan, Hikmet; Pinasco, Juan Pablo; Scarola, Cristian; Energy dependent potential problems for the one dimensional p-Laplacian operator; Pergamon-Elsevier Science Ltd; Nonlinear Analysis-real World Applications; 45; 2-2019; 285-298
1468-1218
CONICET Digital
CONICET
url http://hdl.handle.net/11336/116929
identifier_str_mv Koyunbakan, Hikmet; Pinasco, Juan Pablo; Scarola, Cristian; Energy dependent potential problems for the one dimensional p-Laplacian operator; Pergamon-Elsevier Science Ltd; Nonlinear Analysis-real World Applications; 45; 2-2019; 285-298
1468-1218
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.nonrwa.2018.07.001
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S1468121818305649
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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