On the stability of radial solutions of semilinear elliptic equations in all of Rn

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Regularity of radial minimizers and extremal solutions of semilinear elliptic equations (2005, methodology): “We used the same method in [4] to study the stability or instability of radial solutions in all space.”
Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS (2010, background): “In [35], Cabré and Capella deal with general smooth nonlinearities (convex and increasing) in the radial setting and when ̨ D 0.”
Compactness along the branch of semistable and unstable solutions for an elliptic problem with a singular nonlinearity (2005, background): “singular situation. Theorem 1.3 is based on a blow up argument and the knowledge of linear instability for solutions of a limit problem on RN, a result which is interesting in itself (see for example [8]) and which somehow explains the special role of dimension 7 and α= αN for this problem. Theorem ”
Saddle-shaped solutions of bistable diffusion equations in all of ℝ2m (2009, background): “In higher dimensions, Cabré and Capella [8] have established that, for n ≤ 8 and all f ∈ C1(R), if u is a nonconstant bounded radial solution of (1.”