含时滞的 Herglotz 型变分问题：DuBois-Reymond 条件与 Noether 第一定理
最优化与控制
2015-04-16 v1
摘要
我们将 DuBois-Reymond 必要最优性条件和 Noether 第一定理推广到含时滞的 Herglotz 型变分问题。作为推论，我们的结果给出了最近于 [Numer. Algebra Control Optim. 2 (2012), no. 3, 619-630] 中证明的含时滞变分问题的 DuBois-Reymond 必要最优性条件和第一 Noether 定理。我们的主要结果也是对 [Topol. Methods Nonlinear Anal. 20 (2002), no. 2, 261-273] 中证明的 Herglotz 广义变分原理的第一类 Noether 型定理的推广。
引用
@article{arxiv.1501.04873,
title = {Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether's first theorem},
author = {Simao P. S. Santos and Natalia Martins and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:1501.04873},
year = {2015}
}
备注
This is a preprint of a paper whose final and definite form will be published in the journal Discrete and Continuous Dynamical Systems. Series A, ISSN 1078-0947 (Print), ISSN 1553-5231 (Online). Submitted 01/May/2014; revised 14/Oct/2014; accepted for publication 20/Jan/2015