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Title: Generalizing the variational theory on time scales to include the delta indefinite integral
Author: Martins, N.
Torres, D.F.M.
Keywords: Calculus of variations
EulerLagrange equations
Isoperimetric problems
Natural boundary conditions
Time scales
Issue Date: 2011
Publisher: Elsevier
Abstract: We prove necessary optimality conditions of EulerLagrange 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 kinds of variational problems were considered by Euler himself and have been recently investigated in [J. Gregory, Generalizing variational theory to include the indefinite integral, higher derivatives, and a variety of means as cost variables, Methods Appl. Anal. 15 (4) (2008) 427435]. Our results not only provide a generalization to previous results, but also give some other interesting optimality conditions as special cases. © 2011 Elsevier Ltd. All rights reserved.
Peer review: yes
ISSN: 0898-1221
Appears in Collections:MAT - Artigos

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