On the stability of radial solutions of semilinear elliptic equations in all of R<sup>n</sup>

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Títol:	On the stability of radial solutions of semilinear elliptic equations in all of Rⁿ
Autor/a:	Cabré Vilagut, Xavier; Capella Kort, Antonio
Altres autors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
Abstract:	We establish that every nonconstant bounded radial solution u of −?u = f (u) in all of Rn is unstable if n ? 10. The result applies to every C1 nonlinearity f satisfying a generic nondegeneracy condition. In particular, it applies to every analytic and every power-like nonlinearity. We also give an example of a nonconstant bounded radial solution u which is stable for every n ? 11, and where f is a polynomial. To cite this article: X. Cabré, A. Capella, C. R. Acad. Sci. Paris, Ser. I 338 (2004). ? 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved.
Abstract:	Peer Reviewed
Matèries:	-Partial differential equations -Partial Differential Equations -Equacions en derivades parcials -Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions -Classificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type
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Tipus de document:	Article
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Cabré Vilagut, Xavier; Capella Kort, Antonio

Cabré Vilagut, Xavier; Poggesi, Giorgio

Cabré Vilagut, Xavier; Consul Porras, M. Nieves; Mande Nieto, José Vicente

Cabré Vilagut, Xavier; Lucia, Marcello; Sanchón, Manel; Villegas, Salvador

Cabré Vilagut, Xavier; Roquejoffre, Jean-Michel

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