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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Autor principal: Rossi, Julio Daniel
Publicado: 2004
Materias:
Critical exponents
Nonlinear boundary conditions
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v198_n1_p91_GarciaAzorero
http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p91_GarciaAzorero
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00220396_v198_n1_p91_GarciaAzorero
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spelling paper:paper_00220396_v198_n1_p91_GarciaAzorero2023-06-08T14:45:08Z A convex-concave problem with a nonlinear boundary condition Rossi, Julio Daniel 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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v198_n1_p91_GarciaAzorero 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)
topic Critical exponents
Nonlinear boundary conditions
spellingShingle Critical exponents
Nonlinear boundary conditions
Rossi, Julio Daniel
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.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v198_n1_p91_GarciaAzorero
http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p91_GarciaAzorero
work_keys_str_mv AT rossijuliodaniel aconvexconcaveproblemwithanonlinearboundarycondition
AT rossijuliodaniel convexconcaveproblemwithanonlinearboundarycondition
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