A bifurcation problem governed by the boundary condition i

We deal with positive solutions of Δu = a(x)u p in a bounded smooth domain Ω ⊂ ℝN subject to the boundary condition ∂u/∂ν = λu, λ a parameter, p > 1. We prove that this problem has a unique positive solution if and only if 0 < λ < σ1 where, roughly speaking, σ1 is finite if and...

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Autor principal: Rossi, Julio Daniel
Publicado: 2007
Materias:
Bifurcation
Eigenvalues
Elliptic problems
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10219722_v14_n5-6_p499_GarciaMelian
http://hdl.handle.net/20.500.12110/paper_10219722_v14_n5-6_p499_GarciaMelian
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_10219722_v14_n5-6_p499_GarciaMelian
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spelling paper:paper_10219722_v14_n5-6_p499_GarciaMelian2023-06-08T16:00:04Z A bifurcation problem governed by the boundary condition i Rossi, Julio Daniel Bifurcation Eigenvalues Elliptic problems We deal with positive solutions of Δu = a(x)u p in a bounded smooth domain Ω ⊂ ℝN subject to the boundary condition ∂u/∂ν = λu, λ a parameter, p > 1. We prove that this problem has a unique positive solution if and only if 0 < λ < σ1 where, roughly speaking, σ1 is finite if and only if | ∂ Ω ∩ {a = 0}| > 0 and coincides with the first eigenvalue of an associated eigenvalue problem. Moreover, we find the limit profile of the solution as λ → σ1. © 2007 Birkhaueser. 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_10219722_v14_n5-6_p499_GarciaMelian http://hdl.handle.net/20.500.12110/paper_10219722_v14_n5-6_p499_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
Eigenvalues
Elliptic problems
spellingShingle Bifurcation
Eigenvalues
Elliptic problems
Rossi, Julio Daniel
A bifurcation problem governed by the boundary condition i
topic_facet Bifurcation
Eigenvalues
Elliptic problems
description We deal with positive solutions of Δu = a(x)u p in a bounded smooth domain Ω ⊂ ℝN subject to the boundary condition ∂u/∂ν = λu, λ a parameter, p > 1. We prove that this problem has a unique positive solution if and only if 0 < λ < σ1 where, roughly speaking, σ1 is finite if and only if | ∂ Ω ∩ {a = 0}| > 0 and coincides with the first eigenvalue of an associated eigenvalue problem. Moreover, we find the limit profile of the solution as λ → σ1. © 2007 Birkhaueser.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title A bifurcation problem governed by the boundary condition i
title_short A bifurcation problem governed by the boundary condition i
title_full A bifurcation problem governed by the boundary condition i
title_fullStr A bifurcation problem governed by the boundary condition i
title_full_unstemmed A bifurcation problem governed by the boundary condition i
title_sort bifurcation problem governed by the boundary condition i
publishDate 2007
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10219722_v14_n5-6_p499_GarciaMelian
http://hdl.handle.net/20.500.12110/paper_10219722_v14_n5-6_p499_GarciaMelian
work_keys_str_mv AT rossijuliodaniel abifurcationproblemgovernedbytheboundaryconditioni
AT rossijuliodaniel bifurcationproblemgovernedbytheboundaryconditioni
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