The competition between incoming and outgoing fluxes in an elliptic problem
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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/40060 |
| Acceso en línea: | http://hdl.handle.net/11441/40060 https://doi.org/10.1142/S0219199707002642 |
| Access Level: | acceso abierto |
| Palabra clave: | Elliptic problems nonlinear boundary conditions sub and supersolutions bifurcation |
| Sumario: | 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. |
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