Calculus of variations on time scales: weak local piecewise Crd1 solutions with variable endpoints

By R. Hilscher, V. Zeidan. 2004

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Calculus of variations on time scales with nabla derivatives (2008, background): “For r = 1, problem (P) provides the nabla analog of the delta problem on time scales (1) studied in [3, 4, 13, 14], thus providing, in our opinion, a better formulation than that of [1] (cf.”
An application of time scales to economics (2006, methodology): “The calculus of variation has been studied with the delta notion in the papers by Bohner [3] and Hilscher and Zeidan [4].”