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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| Autores principales: | , , |
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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 https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00220396_v198_n1_p91_GarciaAzorero_oai |
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| Sumario: | 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. |
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