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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2009
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00220396_v247_n3_p779_GarciaMelian https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00220396_v247_n3_p779_GarciaMelian_oai |
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I28-R145-paper_00220396_v247_n3_p779_GarciaMelian_oai2024-08-16 García-Melián, J. Rossi, J.D. Sabina de Lis, J.C. 2009 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. application/pdf http://hdl.handle.net/20.500.12110/paper_00220396_v247_n3_p779_GarciaMelian info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Differ. Equ. 2009;247(3):779-810 Asymptotic profiles Bifurcation Elliptic semilinear systems of competitive type Sub- and supersolutions An elliptic system with bifurcation parameters on the boundary conditions info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00220396_v247_n3_p779_GarciaMelian_oai |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-145 |
| collection |
Repositorio Digital de la Universidad de Buenos Aires (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 García-Melián, J. Rossi, J.D. Sabina de Lis, J.C. 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. |
| format |
Artículo Artículo publishedVersion |
| author |
García-Melián, J. Rossi, J.D. Sabina de Lis, J.C. |
| author_facet |
García-Melián, J. Rossi, J.D. Sabina de Lis, J.C. |
| author_sort |
García-Melián, J. |
| 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 |
http://hdl.handle.net/20.500.12110/paper_00220396_v247_n3_p779_GarciaMelian https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00220396_v247_n3_p779_GarciaMelian_oai |
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