A logistic equation with refuge and nonlocal diffusion
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 support...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_15340392_v8_n6_p2037_GarciaMelian http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_15340392_v8_n6_p2037_GarciaMelian_oai |
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I28-R145-paper_15340392_v8_n6_p2037_GarciaMelian_oai2020-10-19 García-Melián, J. Rossi, J.D. 2009 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. application/pdf http://hdl.handle.net/20.500.12110/paper_15340392_v8_n6_p2037_GarciaMelian info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar Commun. Pure Appl. Anal. 2009;8(6):2037-2053 Logistic problems Nonlocal diffusion A logistic equation with refuge and nonlocal diffusion info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_15340392_v8_n6_p2037_GarciaMelian_oai |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-145 |
| collection |
Repositorio Digital de la Universidad de Buenos Aires (UBA) |
| topic |
Logistic problems Nonlocal diffusion |
| spellingShingle |
Logistic problems Nonlocal diffusion García-Melián, J. Rossi, J.D. A logistic equation with refuge and nonlocal diffusion |
| topic_facet |
Logistic problems Nonlocal diffusion |
| 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. |
| format |
Artículo Artículo publishedVersion |
| author |
García-Melián, J. Rossi, J.D. |
| author_facet |
García-Melián, J. Rossi, J.D. |
| author_sort |
García-Melián, J. |
| title |
A logistic equation with refuge and 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 |
logistic equation with refuge and nonlocal diffusion |
| publishDate |
2009 |
| url |
http://hdl.handle.net/20.500.12110/paper_15340392_v8_n6_p2037_GarciaMelian http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_15340392_v8_n6_p2037_GarciaMelian_oai |
| work_keys_str_mv |
AT garciamelianj alogisticequationwithrefugeandnonlocaldiffusion AT rossijd alogisticequationwithrefugeandnonlocaldiffusion AT garciamelianj logisticequationwithrefugeandnonlocaldiffusion AT rossijd logisticequationwithrefugeandnonlocaldiffusion |
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1766026782081810432 |