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

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/978

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.contributor	Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.contributor.author	Cabré Vilagut, Xavier
dc.contributor.author	Capella Kort, Antonio
dc.date	2003
dc.identifier.citation	C. R. Acad. Sci. Paris, Ser. I 338 (2004) 769–774
dc.identifier.uri	http://hdl.handle.net/2117/978
dc.language.iso	eng
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Partial differential equations
dc.subject	Partial Differential Equations
dc.subject	Equacions en derivades parcials
dc.subject	Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions
dc.subject	Classificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type
dc.title	On the stability of radial solutions of semilinear elliptic equations in all of R<sup>n</sup>
dc.type	info:eu-repo/semantics/article
dc.description.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.
dc.description.abstract	Peer Reviewed

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