A bifurcation problem governed by the boundary condition i
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...
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_10219722_v14_n5-6_p499_GarciaMelian |
| Aporte de: |
| id |
todo:paper_10219722_v14_n5-6_p499_GarciaMelian |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_10219722_v14_n5-6_p499_GarciaMelian2023-10-03T15:56:42Z A bifurcation problem governed by the boundary condition i García-Melián, J. De Lis, J.C.S. Rossi, J.D. Bifurcation Eigenvalues Elliptic problems 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. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10219722_v14_n5-6_p499_GarciaMelian |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Bifurcation Eigenvalues Elliptic problems |
| spellingShingle |
Bifurcation Eigenvalues Elliptic problems García-Melián, J. De Lis, J.C.S. Rossi, J.D. A bifurcation problem governed by the boundary condition i |
| topic_facet |
Bifurcation Eigenvalues Elliptic problems |
| description |
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. |
| format |
JOUR |
| author |
García-Melián, J. De Lis, J.C.S. Rossi, J.D. |
| author_facet |
García-Melián, J. De Lis, J.C.S. Rossi, J.D. |
| author_sort |
García-Melián, J. |
| title |
A bifurcation problem governed by the boundary condition i |
| title_short |
A bifurcation problem governed by the boundary condition i |
| title_full |
A bifurcation problem governed by the boundary condition i |
| title_fullStr |
A bifurcation problem governed by the boundary condition i |
| title_full_unstemmed |
A bifurcation problem governed by the boundary condition i |
| title_sort |
bifurcation problem governed by the boundary condition i |
| url |
http://hdl.handle.net/20.500.12110/paper_10219722_v14_n5-6_p499_GarciaMelian |
| work_keys_str_mv |
AT garciamelianj abifurcationproblemgovernedbytheboundaryconditioni AT delisjcs abifurcationproblemgovernedbytheboundaryconditioni AT rossijd abifurcationproblemgovernedbytheboundaryconditioni AT garciamelianj bifurcationproblemgovernedbytheboundaryconditioni AT delisjcs bifurcationproblemgovernedbytheboundaryconditioni AT rossijd bifurcationproblemgovernedbytheboundaryconditioni |
| _version_ |
1782026945373929472 |