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García-Melián, J.; De Lis, J.C.S.; Rossi, J.D. "A bifurcation problem governed by the boundary condition i" (2007) Nonlinear Differential Equations and Applications. 14(5-6):499-525
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Abstract:

We deal with positive solutions of Δu = a(x)u p in a bounded smooth domain Ω ⊂ ℝN subject to the boundary condition ∂u/∂ν = λu, λ a parameter, p > 1. We prove that this problem has a unique positive solution if and only if 0 < λ < σ1 where, roughly speaking, σ1 is finite if and only if | ∂ Ω ∩ {a = 0}| > 0 and coincides with the first eigenvalue of an associated eigenvalue problem. Moreover, we find the limit profile of the solution as λ → σ1. © 2007 Birkhaueser.

Registro:

Documento: Artículo
Título:A bifurcation problem governed by the boundary condition i
Autor:García-Melián, J.; De Lis, J.C.S.; Rossi, J.D.
Filiación:Dpto. de Análisis Matemático, Universidad de La Laguna, C/ Astrofísico Francisco Sánchez s/n, 38271 - La Laguna, Spain
Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428, Buenos Aires, Argentina
Palabras clave:Bifurcation; Eigenvalues; Elliptic problems
Año:2007
Volumen:14
Número:5-6
Página de inicio:499
Página de fin:525
DOI: http://dx.doi.org/10.1007/s00030-007-4064-x
Título revista:Nonlinear Differential Equations and Applications
Título revista abreviado:Nonlinear Diff. Equ. Appl.
ISSN:10219722
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10219722_v14_n5-6_p499_GarciaMelian

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Citas:

---------- APA ----------
García-Melián, J., De Lis, J.C.S. & Rossi, J.D. (2007) . A bifurcation problem governed by the boundary condition i. Nonlinear Differential Equations and Applications, 14(5-6), 499-525.
http://dx.doi.org/10.1007/s00030-007-4064-x
---------- CHICAGO ----------
García-Melián, J., De Lis, J.C.S., Rossi, J.D. "A bifurcation problem governed by the boundary condition i" . Nonlinear Differential Equations and Applications 14, no. 5-6 (2007) : 499-525.
http://dx.doi.org/10.1007/s00030-007-4064-x
---------- MLA ----------
García-Melián, J., De Lis, J.C.S., Rossi, J.D. "A bifurcation problem governed by the boundary condition i" . Nonlinear Differential Equations and Applications, vol. 14, no. 5-6, 2007, pp. 499-525.
http://dx.doi.org/10.1007/s00030-007-4064-x
---------- VANCOUVER ----------
García-Melián, J., De Lis, J.C.S., Rossi, J.D. A bifurcation problem governed by the boundary condition i. Nonlinear Diff. Equ. Appl. 2007;14(5-6):499-525.
http://dx.doi.org/10.1007/s00030-007-4064-x