Optimality in Infinite-Horizon Variational Problems under Sign Conditions

We consider infinite-horizon variational problems on several spaces of curves. We establish relations between these problems and the properties of their solutions. Notably, we exhibit situations where optimality in a given space of curves implies optimality in a bigger space of curves. We work with a domain of definition of the Lagrangian which has a very general form and we provide assumptions to ensure a satisfactory theory of the necessary conditions of optimality. We apply these results to actualized Lagrangians.     

Calculus of variations in mean and convex lagrangians,III

For the almost periodic or periodic solution of an Euler-Lagrange equation, with a convex lagrangian, under a condition of symmetry on the lagrangian, we establish a necessary condition that involves the second differential of the lagrangian. We deduce from this some results of non-existence.