Abstract:
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.
Registro:
Documento: |
Artículo
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Título: | An elliptic system with bifurcation parameters on the boundary conditions |
Autor: | García-Melián, J.; Rossi, J.D.; Sabina de Lis, J.C. |
Filiación: | Dpto. de Análisis Matemático, Universidad de La Laguna, C/ Astrofisico Francisco Sanchez s/n, 38271 La Laguna, Spain IMDEA Matemáticas, U. Autónoma de Madrid, C-IX, 28049 Madrid, Spain Departamento de Matemática, FCEyN UBA, Ciudad Universitaria, Pab 1, 1428 Buenos Aires, Argentina
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Palabras clave: | Asymptotic profiles; Bifurcation; Elliptic semilinear systems of competitive type; Sub- and supersolutions |
Año: | 2009
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Volumen: | 247
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Número: | 3
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Página de inicio: | 779
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Página de fin: | 810
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DOI: |
http://dx.doi.org/10.1016/j.jde.2009.03.029 |
Título revista: | Journal of Differential Equations
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Título revista abreviado: | J. Differ. Equ.
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ISSN: | 00220396
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CODEN: | JDEQA
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PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00220396_v247_n3_p779_GarciaMelian.pdf |
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v247_n3_p779_GarciaMelian |
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Citas:
---------- APA ----------
García-Melián, J., Rossi, J.D. & Sabina de Lis, J.C.
(2009)
. An elliptic system with bifurcation parameters on the boundary conditions. Journal of Differential Equations, 247(3), 779-810.
http://dx.doi.org/10.1016/j.jde.2009.03.029---------- CHICAGO ----------
García-Melián, J., Rossi, J.D., Sabina de Lis, J.C.
"An elliptic system with bifurcation parameters on the boundary conditions"
. Journal of Differential Equations 247, no. 3
(2009) : 779-810.
http://dx.doi.org/10.1016/j.jde.2009.03.029---------- MLA ----------
García-Melián, J., Rossi, J.D., Sabina de Lis, J.C.
"An elliptic system with bifurcation parameters on the boundary conditions"
. Journal of Differential Equations, vol. 247, no. 3, 2009, pp. 779-810.
http://dx.doi.org/10.1016/j.jde.2009.03.029---------- VANCOUVER ----------
García-Melián, J., Rossi, J.D., Sabina de Lis, J.C. An elliptic system with bifurcation parameters on the boundary conditions. J. Differ. Equ. 2009;247(3):779-810.
http://dx.doi.org/10.1016/j.jde.2009.03.029