A Nonlocal Operator Breaking the Keller-Osserman Condition

This work is concerned about the existence of solutions to the nonlocal semilinear problem - N J (x - y) (u (y) - u (x)) y + h (u (x)) = f (x) x ω u = g x N ω, (-) R N J(x-y)(u(y)-u(x%)), dy+h (u(x)) = f(x),& ω u=g, x R N ω. verifying that lim x → ω x ω u (x) = + ∞ known in the literature as lar...

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Detalles Bibliográficos
Publicado: 2017
Materias:
Keller-Osserman Condition
Large Solutions
Nonlocal Diffusion
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v17_n4_p715_Ferreira
http://hdl.handle.net/20.500.12110/paper_15361365_v17_n4_p715_Ferreira
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_15361365_v17_n4_p715_Ferreira
record_format dspace
spelling paper:paper_15361365_v17_n4_p715_Ferreira2023-06-08T16:20:11Z A Nonlocal Operator Breaking the Keller-Osserman Condition Keller-Osserman Condition Large Solutions Nonlocal Diffusion This work is concerned about the existence of solutions to the nonlocal semilinear problem - N J (x - y) (u (y) - u (x)) y + h (u (x)) = f (x) x ω u = g x N ω, (-) R N J(x-y)(u(y)-u(x%)), dy+h (u(x)) = f(x),& ω u=g, x R N ω. verifying that lim x → ω x ω u (x) = + ∞ known in the literature as large solutions. We find out that the relation between the diffusion and the absorption term is not enough to ensure such existence, not even assuming that the boundary datum g blows up close to ω. On the contrary, the role to obtain large solutions is played only by the interior source f, which gives rise to large solutions even without the presence of the absorption. We determine necessary and sufficient conditions on f providing large solutions and compute the blow-up rates of such solutions in terms of h and f. Finally, we also study the uniqueness of large solutions. © 2017 Walter de Gruyter GmbH, Berlin/Boston 2017. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v17_n4_p715_Ferreira http://hdl.handle.net/20.500.12110/paper_15361365_v17_n4_p715_Ferreira
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Keller-Osserman Condition
Large Solutions
Nonlocal Diffusion
spellingShingle Keller-Osserman Condition
Large Solutions
Nonlocal Diffusion
A Nonlocal Operator Breaking the Keller-Osserman Condition
topic_facet Keller-Osserman Condition
Large Solutions
Nonlocal Diffusion
description This work is concerned about the existence of solutions to the nonlocal semilinear problem - N J (x - y) (u (y) - u (x)) y + h (u (x)) = f (x) x ω u = g x N ω, (-) R N J(x-y)(u(y)-u(x%)), dy+h (u(x)) = f(x),& ω u=g, x R N ω. verifying that lim x → ω x ω u (x) = + ∞ known in the literature as large solutions. We find out that the relation between the diffusion and the absorption term is not enough to ensure such existence, not even assuming that the boundary datum g blows up close to ω. On the contrary, the role to obtain large solutions is played only by the interior source f, which gives rise to large solutions even without the presence of the absorption. We determine necessary and sufficient conditions on f providing large solutions and compute the blow-up rates of such solutions in terms of h and f. Finally, we also study the uniqueness of large solutions. © 2017 Walter de Gruyter GmbH, Berlin/Boston 2017.
title A Nonlocal Operator Breaking the Keller-Osserman Condition
title_short A Nonlocal Operator Breaking the Keller-Osserman Condition
title_full A Nonlocal Operator Breaking the Keller-Osserman Condition
title_fullStr A Nonlocal Operator Breaking the Keller-Osserman Condition
title_full_unstemmed A Nonlocal Operator Breaking the Keller-Osserman Condition
title_sort nonlocal operator breaking the keller-osserman condition
publishDate 2017
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v17_n4_p715_Ferreira
http://hdl.handle.net/20.500.12110/paper_15361365_v17_n4_p715_Ferreira
_version_ 1768546365831380992

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