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Title: A unified approach to the calculus of variations on time scales
Author: Girejko, E.
Malinowska, A.B.
Torres, D.F.M.
Keywords: Calculus of variations
Delta and nabla calculi
Directional derivatives
Euler-Lagrange equations
Time scales
Issue Date: 2010
Publisher: IEEE
Abstract: In this work we propose a new and more general approach to the calculus of variations on time scales that allows to obtain, as particular cases, both delta and nabla results. More precisely, we pose the problem of minimizing or maximizing the composition of delta and nabla integrals with Lagrangians that involve directional derivatives. Unified Euler-Lagrange necessary optimality conditions, as well as sufficient conditions under appropriate convexity assumptions, are proved. We illustrate presented results with simple examples. ©2010 IEEE.
Peer review: yes
ISBN: 978-1-4244-5182-1
Publisher Version:
Appears in Collections:MAT - Comunicações

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