2026-04-13T04:07:29Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/9782025-07-17T10:04:54Zcom_2072_1033col_2072_452950

On the stability of radial solutions of semilinear elliptic equations in all of Rⁿ Cabré Vilagut, Xavier Capella Kort, Antonio Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions 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 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. Peer Reviewed 2003 Article C. R. Acad. Sci. Paris, Ser. I 338 (2004) 769–774 https://hdl.handle.net/2117/978 eng Open Access 6 application/pdf