Natalia Martins
Generalizing the variational theory on time scales to include the delta indefinite integral.
Mon, 02/21/2011 - 16:01 — SomNambulAuthors: Delfim F. M. Torres, Natalia Martins
Subjects: Optimization and Control
AbstractWe prove necessary optimality conditions of Euler-Lagrange type for
generalized problems of the calculus of variations on time scales with a
Lagrangian depending not only on the independent variable, an unknown function
and its delta derivative, but also on a delta indefinite integral that depends
on the unknown function. Such kind of variational problems were considered by
Euler himself and have been recently investigated in [Methods Appl. Anal. 15
(2008), no. 4, 427-435].The Second Euler-Lagrange Equation of Variational Calculus on Time Scales.
Wed, 03/31/2010 - 15:01 — SomNambulAuthors: Delfim F. M. Torres, Zbigniew Bartosiewicz, Natalia Martins
Subjects: Optimization and Control
AbstractThe 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].
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