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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| Outros Autores: | , |
| Formato: | article |
| Idioma: | eng |
| Publicado em: |
2015
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| Assuntos: | |
| Texto completo: | http://hdl.handle.net/10773/14652 |
| País: | Portugal |
| Oai: | oai:ria.ua.pt:10773/14652 |
| Resumo: | 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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