Universitat Politècnica de Catalunya
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
2003
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.
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Article
Inglés
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
Open Access
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