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Title: | Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether's first theorem |
Author: | Santos, S. P. S. Martins, N. Torres, D. F. M. |
Keywords: | DuBois-Reymond necessary optimality condition Euler-Lagrange differential equations Herglotz's calculus of variations Invariance Noether's theorem Time delay |
Issue Date: | Sep-2015 |
Publisher: | American Institute of Mathematical Sciences (AIMS) |
Abstract: | 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]. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/14652 |
DOI: | 10.3934/dcds.2015.35.4593 |
ISSN: | 1078-0947 |
Appears in Collections: | CIDMA - Artigos SCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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[319]Santos_Martins_Torres_DCDS-A.pdf | 390.61 kB | Adobe PDF |
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