The turnpike property for approximate solutions of variational problems without convexity Original Research Article

In this work we study the structure of approximate solutions of variational problems with continuous integrands View the MathML source which belong to a complete metric space of functions View the MathML source. We do not impose any convexity assumption and establish the existence of an everywhere dense Gδ-set View the MathML source such that each integrand in View the MathML source has the turnpike property. This result is an extention of the main result of Zaslavski (Nonlinear Anal. 42 (2000) 1465) which was obtained for integrands View the MathML source which were convex as a function of the last argument (derivative).