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We prove existence of radially symmetric solutions and validity ofEuler-Lagrange necessary conditions for a class of variational problems suchthat neither direct methods nor indirect methods of Calculus of Variationsapply. We obtain existence and qualitative properties of the solutions by meansof ad-hoc superlinear perturbations of the functional having the sameminimizers of the original one.

Non-coercive radially symmetric variational problems: Existence, symmetry and convexity of minimizers