Nonnegative solutions to an elliptic problem with nonlinear absorption and a nonlinear incoming flux on the boundary
In this paper we perform an extensive study of the existence, uniqueness (or multiplicity) and stability of nonnegative solutions to the semilinear elliptic equation −∆u = λu − u p in Ω, with the nonlinear boundary condition ∂u/∂ν = u r on ∂Ω. Here Ω is a smooth bounded domain of IRd with outward un...
| Autores: | , , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2008 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/40064 |
| Acceso en línea: | http://hdl.handle.net/11441/40064 https://doi.org/10.1007/s10231-007-0052-3 |
| Access Level: | acceso abierto |
| Palabra clave: | Elliptic equations Nonlinear boundary conditions |
| Sumario: | In this paper we perform an extensive study of the existence, uniqueness (or multiplicity) and stability of nonnegative solutions to the semilinear elliptic equation −∆u = λu − u p in Ω, with the nonlinear boundary condition ∂u/∂ν = u r on ∂Ω. Here Ω is a smooth bounded domain of IRd with outward unit normal ν, λ is a real parameter and p, r > 0. We also give the precise behavior of solutions for large |λ| in the cases where they exist. The proofs are mainly based on bifurcation techniques, sub-supersolutions and variational methods. |
|---|