Non-Coercive Radially Symmetric Variational Problems: Existence, Symmetry and Convexity of Minimizers
We prove existence of radially symmetric solutions and validity of Euler– Lagrange necessary conditions for a class of variational problems such that neither direct methods nor indirect methods of Calculus of Variations apply. We obtain existence and qualitative properties of the solutions by means of ad-hoc superlinear perturbations of the functional having the same minimizers of the original one.