Perturbation method for non-convex variational problems

Abstract

For a variational problem in a Banach space with quadratic kinetic term and a lower semicontinuous potential, existence of a minimizer is restored by replacing the norm of the space with an equivalent one, arbitrarily close to the original. The form of the problem is preserved; only the norm is perturbed. This extends a result of Ivanov and Zlateva from the convex to the lower semicontinuous case.