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...
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2009
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v11_n4_p585_GarcIaMeliAn http://hdl.handle.net/20.500.12110/paper_02191997_v11_n4_p585_GarcIaMeliAn |
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paper:paper_02191997_v11_n4_p585_GarcIaMeliAn2023-06-08T15:21:35Z Existence and uniqueness of positive solutions to elliptic problems with sublinear mixed boundary conditions Rossi, Julio Daniel 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. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v11_n4_p585_GarcIaMeliAn 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. Rossi, Julio Daniel 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. |
| author |
Rossi, Julio Daniel |
| author_facet |
Rossi, Julio Daniel |
| author_sort |
Rossi, Julio Daniel |
| 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 |
| publishDate |
2009 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v11_n4_p585_GarcIaMeliAn http://hdl.handle.net/20.500.12110/paper_02191997_v11_n4_p585_GarcIaMeliAn |
| work_keys_str_mv |
AT rossijuliodaniel existenceanduniquenessofpositivesolutionstoellipticproblemswithsublinearmixedboundaryconditions |
| _version_ |
1768542594183200768 |