The competition between incoming and outgoing fluxes in an elliptic problem

In this work, we consider existence and uniqueness of positive solutions to the elliptic equation -Δu = λu in Ω, with the nonlinear boundary conditions ∂u/∂v = up on Γ1, ∂u/∂v = -uq on Γ2, where Ω is a smooth bounded domain, ∂Ω = Γ1 ∪ Γ2, Γ̄1 ∩ Γ̄2 = ø, v is the outward unit normal, p, q > 0...

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Detalles Bibliográficos
Autor principal: Rossi, Julio Daniel
Publicado: 2007
Materias:
Bifurcation
Elliptic problems
Nonlinear boundary conditions
Subsolution
Supersolutions
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v9_n6_p781_GarciaMelian
http://hdl.handle.net/20.500.12110/paper_02191997_v9_n6_p781_GarciaMelian
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_02191997_v9_n6_p781_GarciaMelian2023-06-08T15:21:36Z The competition between incoming and outgoing fluxes in an elliptic problem Rossi, Julio Daniel Bifurcation Elliptic problems Nonlinear boundary conditions Subsolution Supersolutions In this work, we consider existence and uniqueness of positive solutions to the elliptic equation -Δu = λu in Ω, with the nonlinear boundary conditions ∂u/∂v = up on Γ1, ∂u/∂v = -uq on Γ2, where Ω is a smooth bounded domain, ∂Ω = Γ1 ∪ Γ2, Γ̄1 ∩ Γ̄2 = ø, v is the outward unit normal, p, q > 0 and λ is a real parameter. We obtain a complete picture of the bifurcation diagram of the problem, depending on the values of p, q and the parameter λ. Our proofs are based on different techniques: variational arguments, bifurcation techniques or comparison arguments, depending on the range of parameters considered. © World Scientific Publishing Company. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2007 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v9_n6_p781_GarciaMelian http://hdl.handle.net/20.500.12110/paper_02191997_v9_n6_p781_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 Bifurcation
Elliptic problems
Nonlinear boundary conditions
Subsolution
Supersolutions
spellingShingle Bifurcation
Elliptic problems
Nonlinear boundary conditions
Subsolution
Supersolutions
Rossi, Julio Daniel
The competition between incoming and outgoing fluxes in an elliptic problem
topic_facet Bifurcation
Elliptic problems
Nonlinear boundary conditions
Subsolution
Supersolutions
description In this work, we consider existence and uniqueness of positive solutions to the elliptic equation -Δu = λu in Ω, with the nonlinear boundary conditions ∂u/∂v = up on Γ1, ∂u/∂v = -uq on Γ2, where Ω is a smooth bounded domain, ∂Ω = Γ1 ∪ Γ2, Γ̄1 ∩ Γ̄2 = ø, v is the outward unit normal, p, q > 0 and λ is a real parameter. We obtain a complete picture of the bifurcation diagram of the problem, depending on the values of p, q and the parameter λ. Our proofs are based on different techniques: variational arguments, bifurcation techniques or comparison arguments, depending on the range of parameters considered. © World Scientific Publishing Company.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title The competition between incoming and outgoing fluxes in an elliptic problem
title_short The competition between incoming and outgoing fluxes in an elliptic problem
title_full The competition between incoming and outgoing fluxes in an elliptic problem
title_fullStr The competition between incoming and outgoing fluxes in an elliptic problem
title_full_unstemmed The competition between incoming and outgoing fluxes in an elliptic problem
title_sort competition between incoming and outgoing fluxes in an elliptic problem
publishDate 2007
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v9_n6_p781_GarciaMelian
http://hdl.handle.net/20.500.12110/paper_02191997_v9_n6_p781_GarciaMelian
work_keys_str_mv AT rossijuliodaniel thecompetitionbetweenincomingandoutgoingfluxesinanellipticproblem
AT rossijuliodaniel competitionbetweenincomingandoutgoingfluxesinanellipticproblem
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