An elliptic system with bifurcation parameters on the boundary conditions

In this paper we consider the elliptic system Δ u = a (x) up vq, Δ v = b (x) ur vs in Ω, a smooth bounded domain, with boundary conditions frac(∂ u, ∂ ν) = λ u, frac(∂ v, ∂ ν) = μ v on ∂Ω. Here λ and μ are regarded as parameters and p, s > 1, q, r > 0 verify (p - 1) (s - 1) > q...

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Detalles Bibliográficos
Autor principal: Rossi, Julio Daniel
Publicado: 2009
Materias:
Asymptotic profiles
Bifurcation
Elliptic semilinear systems of competitive type
Sub- and supersolutions
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v247_n3_p779_GarciaMelian
http://hdl.handle.net/20.500.12110/paper_00220396_v247_n3_p779_GarciaMelian
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00220396_v247_n3_p779_GarciaMelian
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spelling paper:paper_00220396_v247_n3_p779_GarciaMelian2023-06-08T14:45:11Z An elliptic system with bifurcation parameters on the boundary conditions Rossi, Julio Daniel Asymptotic profiles Bifurcation Elliptic semilinear systems of competitive type Sub- and supersolutions In this paper we consider the elliptic system Δ u = a (x) up vq, Δ v = b (x) ur vs in Ω, a smooth bounded domain, with boundary conditions frac(∂ u, ∂ ν) = λ u, frac(∂ v, ∂ ν) = μ v on ∂Ω. Here λ and μ are regarded as parameters and p, s > 1, q, r > 0 verify (p - 1) (s - 1) > q r. We consider the case where a (x) ≥ 0 in Ω and a (x) is allowed to vanish in an interior subdomain Ω0, while b (x) > 0 in over(Ω, -). Our main results include existence of nonnegative nontrivial solutions in the range 0 < λ < λ1 ≤ ∞, μ > 0, where λ1 is characterized by means of an eigenvalue problem, and the uniqueness of such solutions. We also study their asymptotic behavior in all possible cases: as both λ, μ → 0, as λ → λ1 < ∞ for fixed μ (respectively μ → ∞ for fixed λ) and when both λ, μ → ∞ in case λ1 = ∞. © 2009 Elsevier Inc. All rights reserved. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v247_n3_p779_GarciaMelian http://hdl.handle.net/20.500.12110/paper_00220396_v247_n3_p779_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 Asymptotic profiles
Bifurcation
Elliptic semilinear systems of competitive type
Sub- and supersolutions
spellingShingle Asymptotic profiles
Bifurcation
Elliptic semilinear systems of competitive type
Sub- and supersolutions
Rossi, Julio Daniel
An elliptic system with bifurcation parameters on the boundary conditions
topic_facet Asymptotic profiles
Bifurcation
Elliptic semilinear systems of competitive type
Sub- and supersolutions
description In this paper we consider the elliptic system Δ u = a (x) up vq, Δ v = b (x) ur vs in Ω, a smooth bounded domain, with boundary conditions frac(∂ u, ∂ ν) = λ u, frac(∂ v, ∂ ν) = μ v on ∂Ω. Here λ and μ are regarded as parameters and p, s > 1, q, r > 0 verify (p - 1) (s - 1) > q r. We consider the case where a (x) ≥ 0 in Ω and a (x) is allowed to vanish in an interior subdomain Ω0, while b (x) > 0 in over(Ω, -). Our main results include existence of nonnegative nontrivial solutions in the range 0 < λ < λ1 ≤ ∞, μ > 0, where λ1 is characterized by means of an eigenvalue problem, and the uniqueness of such solutions. We also study their asymptotic behavior in all possible cases: as both λ, μ → 0, as λ → λ1 < ∞ for fixed μ (respectively μ → ∞ for fixed λ) and when both λ, μ → ∞ in case λ1 = ∞. © 2009 Elsevier Inc. All rights reserved.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title An elliptic system with bifurcation parameters on the boundary conditions
title_short An elliptic system with bifurcation parameters on the boundary conditions
title_full An elliptic system with bifurcation parameters on the boundary conditions
title_fullStr An elliptic system with bifurcation parameters on the boundary conditions
title_full_unstemmed An elliptic system with bifurcation parameters on the boundary conditions
title_sort elliptic system with bifurcation parameters on the boundary conditions
publishDate 2009
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v247_n3_p779_GarciaMelian
http://hdl.handle.net/20.500.12110/paper_00220396_v247_n3_p779_GarciaMelian
work_keys_str_mv AT rossijuliodaniel anellipticsystemwithbifurcationparametersontheboundaryconditions
AT rossijuliodaniel ellipticsystemwithbifurcationparametersontheboundaryconditions
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