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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| Autores principales: | , |
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| Formato: | Artículo publishedVersion |
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2009
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_15340392_v8_n6_p2037_GarciaMelian https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_15340392_v8_n6_p2037_GarciaMelian_oai |
| Aporte de: |
| Sumario: | 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. |
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