A logistic equation with refuge and nonlocal diffusion
- Autores
- García-Melián, J.; Rossi, J.D.
- Año de publicación
- 2009
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this work we consider the nonlocal stationary nonlinear problem (J * u)(x) - u(x) = -λu(x) + a(x)up(x) in a domain Ω, with the Dirichlet boundary condition u(x) = 0 in ℝN \\ Ω and p > 1. The kernel J involved in the convolution (J * u)(x) = ∫ℝN J(x - y)u(y) dy is a smooth, compactly supported nonnegative function with unit integral, while the weight a(x) is assumed to be nonnegative and is allowed to vanish in a smooth subdomain Ω0 of Ω. Both when a(x) is positive and when it vanishes in a subdomain, we completely discuss the issues of existence and uniqueness of positive solutions, as well as their behavior with respect to the parameter λ.
Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. - Fuente
- Commun. Pure Appl. Anal. 2009;8(6):2037-2053
- Materia
-
Logistic problems
Nonlocal diffusion - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by/2.5/ar
- Repositorio
.jpg)
- Institución
- Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
- OAI Identificador
- paperaa:paper_15340392_v8_n6_p2037_GarciaMelian
Ver los metadatos del registro completo
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A logistic equation with refuge and nonlocal diffusionGarcía-Melián, J.Rossi, J.D.Logistic problemsNonlocal diffusionIn this work we consider the nonlocal stationary nonlinear problem (J * u)(x) - u(x) = -λu(x) + a(x)up(x) in a domain Ω, with the Dirichlet boundary condition u(x) = 0 in ℝN \\ Ω and p > 1. The kernel J involved in the convolution (J * u)(x) = ∫ℝN J(x - y)u(y) dy is a smooth, compactly supported nonnegative function with unit integral, while the weight a(x) is assumed to be nonnegative and is allowed to vanish in a smooth subdomain Ω0 of Ω. Both when a(x) is positive and when it vanishes in a subdomain, we completely discuss the issues of existence and uniqueness of positive solutions, as well as their behavior with respect to the parameter λ.Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2009info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_15340392_v8_n6_p2037_GarciaMelianCommun. Pure Appl. Anal. 2009;8(6):2037-2053reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-09-29T13:42:49Zpaperaa:paper_15340392_v8_n6_p2037_GarciaMelianInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-09-29 13:42:50.639Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse |
| dc.title.none.fl_str_mv |
A logistic equation with refuge and nonlocal diffusion |
| title |
A logistic equation with refuge and nonlocal diffusion |
| spellingShingle |
A logistic equation with refuge and nonlocal diffusion García-Melián, J. Logistic problems Nonlocal diffusion |
| title_short |
A logistic equation with refuge and nonlocal diffusion |
| title_full |
A logistic equation with refuge and nonlocal diffusion |
| title_fullStr |
A logistic equation with refuge and nonlocal diffusion |
| title_full_unstemmed |
A logistic equation with refuge and nonlocal diffusion |
| title_sort |
A logistic equation with refuge and nonlocal diffusion |
| dc.creator.none.fl_str_mv |
García-Melián, J. Rossi, J.D. |
| author |
García-Melián, J. |
| author_facet |
García-Melián, J. Rossi, J.D. |
| author_role |
author |
| author2 |
Rossi, J.D. |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
Logistic problems Nonlocal diffusion |
| topic |
Logistic problems Nonlocal diffusion |
| dc.description.none.fl_txt_mv |
In this work we consider the nonlocal stationary nonlinear problem (J * u)(x) - u(x) = -λu(x) + a(x)up(x) in a domain Ω, with the Dirichlet boundary condition u(x) = 0 in ℝN \\ Ω and p > 1. The kernel J involved in the convolution (J * u)(x) = ∫ℝN J(x - y)u(y) dy is a smooth, compactly supported nonnegative function with unit integral, while the weight a(x) is assumed to be nonnegative and is allowed to vanish in a smooth subdomain Ω0 of Ω. Both when a(x) is positive and when it vanishes in a subdomain, we completely discuss the issues of existence and uniqueness of positive solutions, as well as their behavior with respect to the parameter λ. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. |
| description |
In this work we consider the nonlocal stationary nonlinear problem (J * u)(x) - u(x) = -λu(x) + a(x)up(x) in a domain Ω, with the Dirichlet boundary condition u(x) = 0 in ℝN \\ Ω and p > 1. The kernel J involved in the convolution (J * u)(x) = ∫ℝN J(x - y)u(y) dy is a smooth, compactly supported nonnegative function with unit integral, while the weight a(x) is assumed to be nonnegative and is allowed to vanish in a smooth subdomain Ω0 of Ω. Both when a(x) is positive and when it vanishes in a subdomain, we completely discuss the issues of existence and uniqueness of positive solutions, as well as their behavior with respect to the parameter λ. |
| publishDate |
2009 |
| dc.date.none.fl_str_mv |
2009 |
| 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/20.500.12110/paper_15340392_v8_n6_p2037_GarciaMelian |
| url |
http://hdl.handle.net/20.500.12110/paper_15340392_v8_n6_p2037_GarciaMelian |
| dc.language.none.fl_str_mv |
eng |
| language |
eng |
| dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar |
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openAccess |
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http://creativecommons.org/licenses/by/2.5/ar |
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application/pdf |
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Commun. Pure Appl. Anal. 2009;8(6):2037-2053 reponame:Biblioteca Digital (UBA-FCEN) instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales instacron:UBA-FCEN |
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Biblioteca Digital (UBA-FCEN) |
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Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
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UBA-FCEN |
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Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
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ana@bl.fcen.uba.ar |
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