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Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2014

Nonshifted calculus of variations on time scales with ∇-differentiable σ

Résumé

In calculus of variations on general time scales, an Euler-Lagrange equation of integral form is usually derived in order to characterize the critical points of nonshifted 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 ∇-differentiability of the forward jump operator σ is a sharp assumption on the time scale in order to ∇-differentiate this integral Euler-Lagrange equation. This procedure leads to an Euler-Lagrange equation of differential form. Furthermore, from this differential form, we prove a Noether-type theorem providing an explicit constant of motion for Euler-Lagrange equations admitting a symmetry.
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Dates et versions

hal-01253287 , version 1 (09-01-2016)

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Loïc Bourdin. Nonshifted calculus of variations on time scales with ∇-differentiable σ. Journal of Mathematical Analysis and Applications, 2014, 411 (2), pp.543-554. ⟨10.1016/j.jmaa.2013.10.013⟩. ⟨hal-01253287⟩
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