A convex-concave problem with a nonlinear boundary condition
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 whi...
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| Formato: | Artículo publishedVersion |
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2004
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p91_GarciaAzorero |
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paperaa:paper_00220396_v198_n1_p91_GarciaAzorero2023-06-12T16:43:37Z A convex-concave problem with a nonlinear boundary condition J. Differ. Equ. 2004;198(1):91-128 Garcia-Azorero, J. Peral, I. Rossi, J.D. Critical exponents Nonlinear boundary conditions 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. 2004 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p91_GarciaAzorero |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| topic |
Critical exponents Nonlinear boundary conditions |
| spellingShingle |
Critical exponents Nonlinear boundary conditions Garcia-Azorero, J. Peral, I. Rossi, J.D. A convex-concave problem with a nonlinear boundary condition |
| topic_facet |
Critical exponents Nonlinear boundary conditions |
| 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. |
| format |
Artículo Artículo publishedVersion |
| author |
Garcia-Azorero, J. Peral, I. Rossi, J.D. |
| author_facet |
Garcia-Azorero, J. Peral, I. Rossi, J.D. |
| author_sort |
Garcia-Azorero, J. |
| title |
A convex-concave problem with a nonlinear boundary condition |
| 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 |
convex-concave problem with a nonlinear boundary condition |
| publishDate |
2004 |
| url |
http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p91_GarciaAzorero |
| work_keys_str_mv |
AT garciaazoreroj aconvexconcaveproblemwithanonlinearboundarycondition AT perali aconvexconcaveproblemwithanonlinearboundarycondition AT rossijd aconvexconcaveproblemwithanonlinearboundarycondition AT garciaazoreroj convexconcaveproblemwithanonlinearboundarycondition AT perali convexconcaveproblemwithanonlinearboundarycondition AT rossijd convexconcaveproblemwithanonlinearboundarycondition |
| _version_ |
1769810320543449088 |