A Nonlocal Operator Breaking the Keller-Osserman Condition

Authors
Ferreira, Raúl; Pérez Pérez, Maria Teresa
Publication Year
2017
Language
English
Format
article
Status
Published version
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.
Fil: Ferreira, Raúl. Universidad Complutense de Madrid; España
Fil: Pérez Pérez, Maria Teresa. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Subject
KELLER-OSSERMAN CONDITION
LARGE SOLUTIONS
NONLOCAL DIFFUSION
Matemática Pura
Matemáticas
CIENCIAS NATURALES Y EXACTAS
Access level
Open access
License
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repository
CONICET Digital (CONICET)
Institution
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identifier
oai:ri.conicet.gov.ar:11336/55505