Abstract:
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.
Registro:
Documento: |
Artículo
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Título: | A logistic equation with refuge and nonlocal diffusion |
Autor: | García-Melián, J.; Rossi, J.D. |
Filiación: | Dpto. de Análisis Matemático, Universidad de la Laguna, C/. Astrofísico Francisco Sánchez s/n, 38271 - La Laguna, Spain Dpto. de Matemáticas, FCEyN, Universidad de Buenos Aires, 1428 - Buenos Aires, Argentina
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Palabras clave: | Logistic problems; Nonlocal diffusion |
Año: | 2009
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Volumen: | 8
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Número: | 6
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Página de inicio: | 2037
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Página de fin: | 2053
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DOI: |
http://dx.doi.org/10.3934/cpaa.2009.8.2037 |
Título revista: | Communications on Pure and Applied Analysis
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Título revista abreviado: | Commun. Pure Appl. Anal.
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ISSN: | 15340392
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PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_15340392_v8_n6_p2037_GarciaMelian.pdf |
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15340392_v8_n6_p2037_GarciaMelian |
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Citas:
---------- APA ----------
García-Melián, J. & Rossi, J.D.
(2009)
. A logistic equation with refuge and nonlocal diffusion. Communications on Pure and Applied Analysis, 8(6), 2037-2053.
http://dx.doi.org/10.3934/cpaa.2009.8.2037---------- CHICAGO ----------
García-Melián, J., Rossi, J.D.
"A logistic equation with refuge and nonlocal diffusion"
. Communications on Pure and Applied Analysis 8, no. 6
(2009) : 2037-2053.
http://dx.doi.org/10.3934/cpaa.2009.8.2037---------- MLA ----------
García-Melián, J., Rossi, J.D.
"A logistic equation with refuge and nonlocal diffusion"
. Communications on Pure and Applied Analysis, vol. 8, no. 6, 2009, pp. 2037-2053.
http://dx.doi.org/10.3934/cpaa.2009.8.2037---------- VANCOUVER ----------
García-Melián, J., Rossi, J.D. A logistic equation with refuge and nonlocal diffusion. Commun. Pure Appl. Anal. 2009;8(6):2037-2053.
http://dx.doi.org/10.3934/cpaa.2009.8.2037