Wellposedness in the calculus of variations

We consider the stability of solutions of variational problems with respect to perturbations of the integrand, raised by Ulam in [21]. In this paper we prove some results concerning Ulam's problem by using the theory of wellposedness, We consider the notion of wellposedness introduced in [23] and we deal with perturbations of the integrands related to variational convergence, Moreover some criteria to ol,tain variational convergence of sequences of non-convex integrals are given.