Article
The competition between incoming and outgoing fluxes in an elliptic problem
Author/s | García Melián, Jorge José
Rossi Pérez, Julio Daniel Suárez Fernández, Antonio |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2007 |
Deposit Date | 2016-04-19 |
Published in |
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Abstract | In this work we consider existence and uniqueness of positive solutions to the elliptic equation −∆u = λu in Ω, with the nonlinear boundary conditions ∂u
∂ν = u p on Γ1, ∂u ∂ν = −u q on Γ2, where Ω is a smooth bounded ... In this work we consider existence and uniqueness of positive solutions to the elliptic equation −∆u = λu in Ω, with the nonlinear boundary conditions ∂u ∂ν = u p on Γ1, ∂u ∂ν = −u q on Γ2, where Ω is a smooth bounded domain, ∂Ω = Γ1 ∪ Γ2, Γ1 ∩ Γ2 = ∅, ν 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. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) |
Project ID. | MTM2005-06480
BFM 2003-06446 MTM2006-07932 ANPCyT PICT |
Citation | García Melián, J.J., Rossi Pérez, J.D. y Suárez Fernández, A. (2007). The competition between incoming and outgoing fluxes in an elliptic problem. Communications in Contemporary Mathematics, 9 (6), 781-810. |
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