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.
CitationC. R. Acad. Sci. Paris, Ser. I 338 (2004) 769–774
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