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

By Simão P. S. Santos, Natália Martins, Delfim F. M. Torres. 2015

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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].

Subfields: Applied Mathematics, Computational Theory and Mathematics

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