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 Generalizing the variational theory on time scales to include the delta indefinite integral
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/4063

title: Generalizing the variational theory on time scales to include the delta indefinite integral
authors: 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.
URI: http://hdl.handle.net/10773/4063
ISSN: 0898-1221
source: Computers and Mathematics with Applications
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