Generalizing the variational theory on time scales to include the delta indefinite integral
Abstract
We 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]. Our results not only provide a generalization to previous results, but also give some other interesting optimality conditions as special cases.
Cite
@article{arxiv.1102.3727,
title = {Generalizing the variational theory on time scales to include the delta indefinite integral},
author = {Natalia Martins and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:1102.3727},
year = {2011}
}
Comments
Submitted 25-Jul-2010; revised 27-Nov-2010; accepted 16-Feb-2011; for publication in Computers and Mathematics with Applications