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Title: The second Euler-Lagrange equation of variational calculus on time scales
Author: Bartosiewicz, Z.
Martins, N.
Torres, D.F.M.
Keywords: Calculus of variations
DuBois-Reymond, and second Erdmann necessary optimality conditions
Noether's theorem
Optimal control
Time scales
Issue Date: 2011
Publisher: Lavoisier - Hermes Science Publications
Abstract: The fundamental problem of the calculus of variations on time scales concerns the minimization of a delta-integral over all trajectories satisfying given boundary conditions. In this paper, we prove the second Euler-Lagrange necessary optimality condition for optimal trajectories of variational problems on time scales. As an example of application of the main result, we give an alternative and simpler proof to the Noether theorem on time scales recently obtained in [J. Math. Anal. Appl. 342 (2008), no. 2, 1220-1226]. © 2011 EUCA.
Peer review: yes
ISSN: 0947-3580
Appears in Collections:DMat - Artigos

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