A convex-concave problem with a nonlinear boundary condition
- Autores
- Garcia-Azorero, J.; Peral, I.; Rossi, J.D.
- Año de publicación
- 2004
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this paper we study the existence of nontrivial solutions of the problem {-Δu+u = u p-2u in Ω, {∂u/∂v = λ u q-2u on ∂Ω, with 1<q<2(N-1)/(N-2) and 1<p≤2N/(N-2). In the concave-convex case, i.e., 1<q<2<p, if λ is small there exist two positive solutions while for λ large there is no positive solution. When p is critical, and q subcritical we obtain existence results using the concentration compactness method. Finally, we apply the implicit function theorem to obtain solutions for λ small near u0 = 1. © 2003 Elsevier Science (USA). All rights reserved.
Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. - Fuente
- J. Differ. Equ. 2004;198(1):91-128
- Materia
-
Critical exponents
Nonlinear boundary conditions - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by/2.5/ar
- Repositorio
.jpg)
- Institución
- Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
- OAI Identificador
- paperaa:paper_00220396_v198_n1_p91_GarciaAzorero
Ver los metadatos del registro completo
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A convex-concave problem with a nonlinear boundary conditionGarcia-Azorero, J.Peral, I.Rossi, J.D.Critical exponentsNonlinear boundary conditionsIn this paper we study the existence of nontrivial solutions of the problem {-Δu+u = u p-2u in Ω, {∂u/∂v = λ u q-2u on ∂Ω, with 1<q<2(N-1)/(N-2) and 1<p≤2N/(N-2). In the concave-convex case, i.e., 1<q<2<p, if λ is small there exist two positive solutions while for λ large there is no positive solution. When p is critical, and q subcritical we obtain existence results using the concentration compactness method. Finally, we apply the implicit function theorem to obtain solutions for λ small near u0 = 1. © 2003 Elsevier Science (USA). All rights reserved.Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2004info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p91_GarciaAzoreroJ. Differ. Equ. 2004;198(1):91-128reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-10-16T09:30:16Zpaperaa:paper_00220396_v198_n1_p91_GarciaAzoreroInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-10-16 09:30:18.206Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse |
| dc.title.none.fl_str_mv |
A convex-concave problem with a nonlinear boundary condition |
| title |
A convex-concave problem with a nonlinear boundary condition |
| spellingShingle |
A convex-concave problem with a nonlinear boundary condition Garcia-Azorero, J. Critical exponents Nonlinear boundary conditions |
| title_short |
A convex-concave problem with a nonlinear boundary condition |
| title_full |
A convex-concave problem with a nonlinear boundary condition |
| title_fullStr |
A convex-concave problem with a nonlinear boundary condition |
| title_full_unstemmed |
A convex-concave problem with a nonlinear boundary condition |
| title_sort |
A convex-concave problem with a nonlinear boundary condition |
| dc.creator.none.fl_str_mv |
Garcia-Azorero, J. Peral, I. Rossi, J.D. |
| author |
Garcia-Azorero, J. |
| author_facet |
Garcia-Azorero, J. Peral, I. Rossi, J.D. |
| author_role |
author |
| author2 |
Peral, I. Rossi, J.D. |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
Critical exponents Nonlinear boundary conditions |
| topic |
Critical exponents Nonlinear boundary conditions |
| dc.description.none.fl_txt_mv |
In this paper we study the existence of nontrivial solutions of the problem {-Δu+u = u p-2u in Ω, {∂u/∂v = λ u q-2u on ∂Ω, with 1<q<2(N-1)/(N-2) and 1<p≤2N/(N-2). In the concave-convex case, i.e., 1<q<2<p, if λ is small there exist two positive solutions while for λ large there is no positive solution. When p is critical, and q subcritical we obtain existence results using the concentration compactness method. Finally, we apply the implicit function theorem to obtain solutions for λ small near u0 = 1. © 2003 Elsevier Science (USA). All rights reserved. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. |
| description |
In this paper we study the existence of nontrivial solutions of the problem {-Δu+u = u p-2u in Ω, {∂u/∂v = λ u q-2u on ∂Ω, with 1<q<2(N-1)/(N-2) and 1<p≤2N/(N-2). In the concave-convex case, i.e., 1<q<2<p, if λ is small there exist two positive solutions while for λ large there is no positive solution. When p is critical, and q subcritical we obtain existence results using the concentration compactness method. Finally, we apply the implicit function theorem to obtain solutions for λ small near u0 = 1. © 2003 Elsevier Science (USA). All rights reserved. |
| publishDate |
2004 |
| dc.date.none.fl_str_mv |
2004 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
| status_str |
publishedVersion |
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http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p91_GarciaAzorero |
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http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p91_GarciaAzorero |
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eng |
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eng |
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info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar |
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openAccess |
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http://creativecommons.org/licenses/by/2.5/ar |
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application/pdf |
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Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
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UBA-FCEN |
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Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
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