Geodesic
Inverse Problem of the Calculus of Variations for Systems of Differential-Difference Equations of Second Order
Matematičeskie zametki, Tome 72 (2002) no. 5, pp. 745-749.

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The inverse problem of the calculus of variations for second-order nonlinear and linear systems of differential-difference equations is considered. The relationship between the formal potentiality of a linear system with constant coefficients and the parity of its characteristic function is established. 
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A. M. Popov. Inverse Problem of the Calculus of Variations for Systems of Differential-Difference Equations of Second Order. Matematičeskie zametki, Tome 72 (2002) no. 5, pp. 745-749. http://geodesic.mathdoc.fr/item/MZM_2002_72_5_a13/

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