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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
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
Palabras clave:Asymptotic profiles; Bifurcation; Elliptic semilinear systems of competitive type; Sub- and supersolutions
Año:2009
Volumen:247
Número:3
Página de inicio:779
Página de fin:810
DOI: http://dx.doi.org/10.1016/j.jde.2009.03.029
Título revista:Journal of Differential Equations
Título revista abreviado:J. Differ. Equ.
ISSN:00220396
CODEN:JDEQA
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