2015/01/01 by Simao P. S. Santos, Simão P. S. Santos, Natália Martins +2 · 48 citations
Computer Science · Mathematics · #Applied mathematics #Generalization #Lagrangian #Mathematical analysis #Mathematical physics #Mathematics #Noether's theorem #Nonlinear Differential Equations Analysis #Nonlinear system #Optimization and Variational Analysis #Physics #Polynomial and algebraic computation #Pure mathematics #Quantum mechanics #Type (biology) #Variational principle #math.OC #msc:34H05 #msc:49K15 #msc:49S05
paper · pdf · doi:10.3934/dcds.2015.35.4593
published in Discrete and Continuous Dynamical Systems 35(9), 4593-4610 (American Institute of Mathematical Sciences) · 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
openalex publication_date 2015/01/01 · arxiv created 2015/01/20 · arxiv updated 2015/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We extend the DuBois--Reymond necessary optimality conditionand Noether's first theorem to variational problems of Herglotztype with time delay. Our results provide, as corollaries,the DuBois--Reymond necessary optimality condition and the firstNoether theorem for variational problems with time delay recentlyproved in [Numer. Algebra Control Optim. 2 (2012), no. 3, 619--630].Our main result is also a generalization of the first Noether-type theoremfor the generalized variational principle of Herglotz proved in[Topol. Methods Nonlinear Anal. 20 (2002), no. 2, 261--273].