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 properti
es of the extremals which are independent of the length of the interval, fo
r all sufficiently large intervals. As in [12, 13] the study of these prope
rties is based on the relation between the variational problem on bounded,
large intervals and a limiting problem on R+. Our investigation employs tec
hniques developed in [10, 12, 13] along with turnpike techniques developed
in [16, 17]. (C) Elsevier, Paris.