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http://hdl.handle.net/10773/4063
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 |
URI: | http://hdl.handle.net/10773/4063 |
ISSN: | 0898-1221 |
Appears in Collections: | DMat - Artigos |
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File | Description | Size | Format | |
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[198]Generalizing_variational_theory_ts_delta_indefinite_integral.pdf | 270.07 kB | Adobe PDF |
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