Generic well-posedness of variational problems without convexity assumptions

The Tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands f which satisfy convexity and growth conditions. In our previous work a generic well-posedness result (with respect to variations of the integrand of the integral functional) without the convexity condition was established for a class of optimal control problems satisfying the Cesari growth condition. In this paper we extend this generic well-posedness result to two classes of variational problems in which the values at the end points are also subject to variations. The main results of the paper are obtained as realizations of a general variational principle. (C) 2003 Elsevier Science (USA). All rights reserved.