Non shifted calculus of variations on time scales with Nabla-differentiable Sigma
Abstract
In calculus of variations on general time scales, an integral Euler-Lagrange equation is usually derived in order to characterize the critical points of non shifted Lagrangian functionals, see e.g. [R.A.C. Ferreira and co-authors, Optimality conditions for the calculus of variations with higher-order delta derivatives, Appl. Math. Lett., 2011]. In this paper, we prove that the Nabla-differentiability of the forward jump operator Sigma is a sharp assumption in order to obtain an Euler-Lagrange equation of differential form. Furthermore, this differential form allows us to prove a Noether-type theorem providing an explicit constant of motion for differential Euler-Lagrange equations admitting a symmetry.
Keywords
Cite
@article{arxiv.1302.3623,
title = {Non shifted calculus of variations on time scales with Nabla-differentiable Sigma},
author = {Loïc Bourdin},
journal= {arXiv preprint arXiv:1302.3623},
year = {2016}
}
Comments
This is a preprint of a paper whose final and definite form is published in Journal of Mathematical Analysis and Applications