Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether's first theorem

We extend the DuBois-Reymond necessary optimality condition and Noether's first theorem to variational problems of Herglotz type with time delay. Our results provide, as corollaries, the DuBois-Reymond necessary optimality condition and the first Noether theorem for variational problems with ti...

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Bibliographic Details
Main Author: Santos, S. P. S. (author)
Other Authors: Martins, N. (author), Torres, D. F. M. (author)
Format: article
Language:eng
Published: 2015
Subjects:
DuBois-Reymond necessary optimality condition
Euler-Lagrange differential equations
Herglotz's calculus of variations
Invariance
Noether's theorem
Time delay
Online Access:http://hdl.handle.net/10773/14652
Country:Portugal
Oai:oai:ria.ua.pt:10773/14652
Description
Summary:We extend the DuBois-Reymond necessary optimality condition and Noether's first theorem to variational problems of Herglotz type with time delay. Our results provide, as corollaries, the DuBois-Reymond necessary optimality condition and the first Noether theorem for variational problems with time delay recently proved in [Numer. Algebra Control Optim. 2(2012), no. 3, 619-630]. Our main result is also a generalization of the first Noether-type theorem for the generalized variational principle of Herglotz proved in [Topol. Methods Nonlinear Anal. 20(2002), no. 2, 261-273].

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