Abstract:
In this work, we consider existence and uniqueness of positive solutions to the elliptic equation -Δu = λu in Ω, with the nonlinear boundary conditions ∂u/∂v = up on Γ1, ∂u/∂v = -uq on Γ2, where Ω is a smooth bounded domain, ∂Ω = Γ1 ∪ Γ2, Γ̄1 ∩ Γ̄2 = ø, v is the outward unit normal, p, q > 0 and λ is a real parameter. We obtain a complete picture of the bifurcation diagram of the problem, depending on the values of p, q and the parameter λ. Our proofs are based on different techniques: variational arguments, bifurcation techniques or comparison arguments, depending on the range of parameters considered. © World Scientific Publishing Company.
Registro:
Documento: |
Artículo
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Título: | The competition between incoming and outgoing fluxes in an elliptic problem |
Autor: | García-Melián, J.; Rossi, J.D.; Suárez, A. |
Filiación: | Dpto. de Análisis Matemático, Universidad de La Laguna, C/. Astrofísico Francisco Sanchez s/n, 38271 La Laguna, Spain Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428, Buenos Aires, Argentina Instituto de Matemáticas y Física Fundamental, CSIC, C/. Serrano 123, 28006, Madrid, Spain Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Fac. de Matemáticas, Univ. de Sevilla, C/. Tarfia s/n, 41012, Sevilla, Spain
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Palabras clave: | Bifurcation; Elliptic problems; Nonlinear boundary conditions; Subsolution; Supersolutions |
Año: | 2007
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Volumen: | 9
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Número: | 6
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Página de inicio: | 781
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Página de fin: | 810
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DOI: |
http://dx.doi.org/10.1142/S0219199707002642 |
Título revista: | Communications in Contemporary Mathematics
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Título revista abreviado: | Commun. Contemp. Math.
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ISSN: | 02191997
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v9_n6_p781_GarciaMelian |
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Citas:
---------- APA ----------
García-Melián, J., Rossi, J.D. & Suárez, A.
(2007)
. The competition between incoming and outgoing fluxes in an elliptic problem. Communications in Contemporary Mathematics, 9(6), 781-810.
http://dx.doi.org/10.1142/S0219199707002642---------- CHICAGO ----------
García-Melián, J., Rossi, J.D., Suárez, A.
"The competition between incoming and outgoing fluxes in an elliptic problem"
. Communications in Contemporary Mathematics 9, no. 6
(2007) : 781-810.
http://dx.doi.org/10.1142/S0219199707002642---------- MLA ----------
García-Melián, J., Rossi, J.D., Suárez, A.
"The competition between incoming and outgoing fluxes in an elliptic problem"
. Communications in Contemporary Mathematics, vol. 9, no. 6, 2007, pp. 781-810.
http://dx.doi.org/10.1142/S0219199707002642---------- VANCOUVER ----------
García-Melián, J., Rossi, J.D., Suárez, A. The competition between incoming and outgoing fluxes in an elliptic problem. Commun. Contemp. Math. 2007;9(6):781-810.
http://dx.doi.org/10.1142/S0219199707002642