Existence and uniqueness of positive solutions to elliptic problems with sublinear mixed boundary conditions
In this work, we consider a class of semilinear elliptic problems with nonlinear boundary conditions of mixed type. Under some monotonicity properties of the nonlinearities involved, we show that positive solutions are unique, and that their existence is characterized by the sign of some associated...
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_02191997_v11_n4_p585_GarcIaMeliAn |
| Aporte de: |
| id |
todo:paper_02191997_v11_n4_p585_GarcIaMeliAn |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_02191997_v11_n4_p585_GarcIaMeliAn2023-10-03T15:11:04Z Existence and uniqueness of positive solutions to elliptic problems with sublinear mixed boundary conditions GarcÍa-MeliÁn, J. Rossi, J.D. Sabina De Lis, J.C. Elliptic equations Mixed boundary conditions Nonlinear boundary conditions Sublinear problems Variational methods; bifurcation. In this work, we consider a class of semilinear elliptic problems with nonlinear boundary conditions of mixed type. Under some monotonicity properties of the nonlinearities involved, we show that positive solutions are unique, and that their existence is characterized by the sign of some associated eigenvalues. One of the most important contributions of this work relies on the fact that we deal with boundary conditions of the form ∂ μ/∂ν = g(x,u) on Γ and u = 0 on Γ', where ν is the outward unit normal to Γ while Γ,Γ' are open, Γ ∩ Γ' = ∅, ∂Ω = Γ ̄∩ Γ̄'but Γ ̄ Γ̄' need not be disjoint. © 2009 World Scientific Publishing Company. 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_02191997_v11_n4_p585_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 |
Elliptic equations Mixed boundary conditions Nonlinear boundary conditions Sublinear problems Variational methods; bifurcation. |
| spellingShingle |
Elliptic equations Mixed boundary conditions Nonlinear boundary conditions Sublinear problems Variational methods; bifurcation. GarcÍa-MeliÁn, J. Rossi, J.D. Sabina De Lis, J.C. Existence and uniqueness of positive solutions to elliptic problems with sublinear mixed boundary conditions |
| topic_facet |
Elliptic equations Mixed boundary conditions Nonlinear boundary conditions Sublinear problems Variational methods; bifurcation. |
| description |
In this work, we consider a class of semilinear elliptic problems with nonlinear boundary conditions of mixed type. Under some monotonicity properties of the nonlinearities involved, we show that positive solutions are unique, and that their existence is characterized by the sign of some associated eigenvalues. One of the most important contributions of this work relies on the fact that we deal with boundary conditions of the form ∂ μ/∂ν = g(x,u) on Γ and u = 0 on Γ', where ν is the outward unit normal to Γ while Γ,Γ' are open, Γ ∩ Γ' = ∅, ∂Ω = Γ ̄∩ Γ̄'but Γ ̄ Γ̄' need not be disjoint. © 2009 World Scientific Publishing Company. |
| format |
JOUR |
| author |
GarcÍa-MeliÁn, J. Rossi, J.D. Sabina De Lis, J.C. |
| author_facet |
GarcÍa-MeliÁn, J. Rossi, J.D. Sabina De Lis, J.C. |
| author_sort |
GarcÍa-MeliÁn, J. |
| title |
Existence and uniqueness of positive solutions to elliptic problems with sublinear mixed boundary conditions |
| title_short |
Existence and uniqueness of positive solutions to elliptic problems with sublinear mixed boundary conditions |
| title_full |
Existence and uniqueness of positive solutions to elliptic problems with sublinear mixed boundary conditions |
| title_fullStr |
Existence and uniqueness of positive solutions to elliptic problems with sublinear mixed boundary conditions |
| title_full_unstemmed |
Existence and uniqueness of positive solutions to elliptic problems with sublinear mixed boundary conditions |
| title_sort |
existence and uniqueness of positive solutions to elliptic problems with sublinear mixed boundary conditions |
| url |
http://hdl.handle.net/20.500.12110/paper_02191997_v11_n4_p585_GarcIaMeliAn |
| work_keys_str_mv |
AT garciamelianj existenceanduniquenessofpositivesolutionstoellipticproblemswithsublinearmixedboundaryconditions AT rossijd existenceanduniquenessofpositivesolutionstoellipticproblemswithsublinearmixedboundaryconditions AT sabinadelisjc existenceanduniquenessofpositivesolutionstoellipticproblemswithsublinearmixedboundaryconditions |
| _version_ |
1807317341247111168 |