A logistic equation with refuge and nonlocal diffusion

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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 suppor...

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Autores principales: García-Melián, J., Rossi, J.D.
Formato: JOUR
Materias:
Logistic problems
Nonlocal diffusion
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_15340392_v8_n6_p2037_GarciaMelian
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_15340392_v8_n6_p2037_GarciaMelian
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spelling todo:paper_15340392_v8_n6_p2037_GarciaMelian2023-10-03T16:21:38Z A logistic equation with refuge and nonlocal diffusion García-Melián, J. Rossi, J.D. Logistic problems 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 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_15340392_v8_n6_p2037_GarciaMelian
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (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 JOUR
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
url http://hdl.handle.net/20.500.12110/paper_15340392_v8_n6_p2037_GarciaMelian
work_keys_str_mv AT garciamelianj alogisticequationwithrefugeandnonlocaldiffusion
AT rossijd alogisticequationwithrefugeandnonlocaldiffusion
AT garciamelianj logisticequationwithrefugeandnonlocaldiffusion
AT rossijd logisticequationwithrefugeandnonlocaldiffusion
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