Weak Local Extrema in Infinite Horizon Optimal Control Problems

In this paper we deal with infinite horizon optimal control problems. Basing on weak variations in an extremal problem in weighted Lebesgue and Sobolev spaces we prove necessary conditions in form of the adjoint equation and a variational inequality. The obtained optimality conditions imply several transversality conditions and the validity of Mangasarian and Arrow type sufficiency conditions. Moreover, a differential game with Weibull distributed cost functionals is considered.