Higher-order variational problems of Herglotz type with time delay

Abstract

We study, using an optimal control point of view, higher-order variational problems of Herglotz type with time delay. Main results are higher-order Euler-Lagrange and DuBois-Reymond necessary optimality conditions as well as a higher-order Noether type theorem for delayed variational problems of Herglotz type.

This is a preprint of a paper whose final and definite form will be published in the International Journal 'Pure and Applied Functional Analysis', ISSN 2189-3756 (print), ISSN 2189-3764 (online). Submitted 01-Dec-2015; revised 12-Mar-2016; accepted for publication 13-Mar-2016. Minor corrections, detected during the reading of the proofs, were done in this second version of the preprint