The asymptotic turnpike property and the uniqueness of a periodic minimal solution for one-dimensional variational problems

Abstract

In the article we consider the asymptotic behaviour of extremals for a class of second order infinite horizon variational problems arising in continuum mechanics. We analyze the uniqueness of a periodic minimal solution and the asymptotic turnpike property which means that all good functions have the same set of limit points.

Keywords:

• Turnpike property
• An (f)-good function
• A minimal long-run average cost growth rate
• The representation formula
• Mathematics Subject Classification 2000: 49J99