The structure of approximate solutions of variational problems without convexity

In this work we study the structure of approximate solutions of variational problems with continuous integrands f : [0,∞) ×Rn ×Rn →R1 which belong to a complete metric space of functions. We do not impose any convexity assumption. The main result in this paper deals with the turnpike property of variational problems. To have this property means that the approximate solutions of the problems are determined mainly by the integrand, and are essentially independent of the choice of interval and endpoint conditions, except in regions close to the endpoints.  2004 Elsevier Inc. All rights reserved.