The structure of extremals of a class of second order variational problems

We study the structure of extremals of a class of second order variational problems without convexity, on intervals in R+. The problems are related to a model in thermodynamics introduced in [7]. We are interested in properties of the extremals which are independent of the length of the interval, for all sufficiently large intervals. As in [12, 13] the study of these properties is based on the relation between the variational problem on bounded, large intervals and a limiting problem on R+. Our investigation employs techniques developed in [10, 12, 13] along with turnpike techniques developed in [16, 17]. (C) Elsevier, Paris.